OK, that gives us a place to start...
OK, so the reason I asked that is because often people look at antenna gain figures only. They figure more must be better. It doesn't always work out that way. There are situations where a really high gain antenna can work against you. Back when I was active on GMRS (and still am a bit on amateur) I used low gain antenna. I'm located in the bottom of a valley with 1000 - 2000 foot high hills all around, none more than a few miles in any direction. The only direction that doesn't have hills is the Pacific Ocean. In that specific case, using a high gain antenna would have been a waste of money. Since my "radio horizon" was pretty close, and in most cases above me, a lower gain, lower cost antenna was all I really needed.
Vertical omni-directional antennas get their gain by flatting out the radiation pattern and focusing it more towards the horizon. Think of a lighthouse. A 500 watt bulb in a lighthouse wouldn't do much on it's own, but when you focus that light just at the horizon, it works pretty well. That works great for a ship out on the horizon, they see a bright light (strong signal). But, if you are on a hill top, you'll still see the light house, but the light won't be as bright since it isn't focused in your direction. On the flip side, if you are on a hill a few miles away and you need to see that light, a 500 watt light bulb that is allowed to spread out a little bit more will be easier to see. Lower gain antennas are like this, they don't compress the radiation pattern so much, allowing more of the RF energy to spread out above and below the horizon.
In your case, a higher gain antenna makes sense. In my case, a lower gain/lower cost antenna worked well.
So, I'd recommend looking for a higher gain antenna.
OK, see above, higher gain antenna will send more of your signal out to the horizon, which sounds like what you want.
As for mounting height, you are good up to 200 feet, unless you have an airport nearby, then the FAA gets involved.
$500 is a reasonable budget for a hobbyist. Does that include the coaxial cable, or just the antenna?
Here's why:
At UHF frequencies, you will lose a lot more signal in your coaxial cable than you would on CB frequencies. Where 50 feet of RG-8 coaxial cable may have been acceptable for your CB antenna, you really want something better for GMRS.
At 27 MHz, 50 feet of RG-8 type cable will lose about 0.5dB of signal just to feed line losses, that's before it even reaches your antenna. That works in both directions, so not only do you lose transmit power, but you lose some of your received signal. Or, for 4 watts RF output from your CB, 3.6 watts actually make it to the antenna.
Not a big deal, perfectly acceptable and reasonable.
Now, change that to 462MHz:
Feed line losses jump to 2.29dB for a 50 foot run. If you were running a 4 watt GMRS radio (I know, you'll run more, but humor me), you'd get 2.4 watts out at the end of the cable. And, again, that works both ways, so you lose nearly 35% of your power both on TX and receive.
For GMRS, you really need to be looking at a higher grade coaxial cable to counteract the feed line losses. This can get a bit expensive, but it's something you need to figure in.
Let's take Times Microwave LMR-600 cable. It's about as big as you can go and still work with it in a residence. Larger than this and the bend radius gets to be large
LMR-600 would give you less than 1dB loss for a 50 foot run at 462MHz. Or, about 18% loss.
LMR-400 is popular with the hobby crowd. It's OK cable, but you can do better for a bit more cost. At UHF frequencies, LMR-400 is still going to lose about 27%, so not necessarily a good choice.
If your coaxial cable runs are longer than 50 feet, then your losses increase with it. At UHF frequencies you need to be looking at high grade cable.
So, figure $150 for cable and supplies, and that still leaves you with $350 for a good antenna. That's still pretty reasonable.
To be fair, there are better coaxial cables available than the LMR-600. If I was doing a similar installation, I'd run nothing less than 1/2 inch Heliax cable. It's a rigid/corrugated cable that can be a bit tough to work with as it's kind of stiff. It's slightly better than the LMR-600, but might not be worth the extra cost and struggles for hobby use.
Also, pay close attention to how you connect this coax up to the radio and antenna. The stiffer cables like LMR-600 or 1/2" Heliax are rarely used to directly connect to radios and antennas in the professional realm. It's usually a really good way to snap off antenna connectors. It's common practice to use a short run of a smaller, more flexible cable to act as a jumper between the radio and coaxial cable run and between the cable run and the antenna. This will protect the antenna connector on your radio and allow you to move the radio around as needed. You don't want to try connecting LMR-600 directly to the radio. You will regret it.
UHF is mostly line of sight, so the higher the better when you are down on the flat lands. Look on line for a "distance to horizon" calculator. That'll let you put in your antenna height and tell you how far off the "radio horizon" is. Make sure to figure in the height of the antenna at the other end.
OK, just wanted to make sure I didn't waste all this typing if you were a 70 year old Grandma who only drives to church on Sundays. Sounds like you are in the right place to do this.
So, PRC made a good suggestion for a reasonably priced antenna. Personal opinion on my end is that I wouldn't go through all this to put up a Chinese made antenna in a place where you get snow/ice and maybe high winds. I've looked at the Tram/Browning brand mobile antennas and I'm not impressed with the quality. Their base antennas might be better, but I'm not sure. What you can find on low cost antennas is that when they are at the factory, they don't spend a lot of labor on actually getting them tuned properly for the intended frequency. This can lead to problems. If you are going to go through the effort to install a base antenna at 30 feet (or higher) and want it to last many years, then you might want to look at a true commercial antenna, not a hobby/amateur grade antenna. While many of them work well, the longevity of them might be in question. It's a decision you'll need to make. If you are comfortable with a $500 budget, then I'd consider going with something better than a $70 Chinese made antenna.
When I was active on GMRS, I used ComTelco base antenna at my house. I'm a few miles from the ocean, so corrosion is always a concern. Not usually high winds and no snow/ice loading, so not really a problem for me. Since I was down in a valley, I went with a 3dB gain base antenna. It was about 24 inches tall and worked well for me.
I'd suggest you look at something from the commercial market, USA made and backed up by a reputable company.
Maybe fish around over at
www.tessco.com for some of the commercial stuff.
Another option is over at "The Antenna Farm". They are a reputable company:
Some brands to consider:
PCTel
Laird
http://www.theantennafarm.com/catalog/laird-technologies-fg4607-8031.html
RFS
What you invest in your antenna system (coaxial cable, mounting, antenna) is going to pay off in the long run if you plan on sticking with GMRS for the long term. However, if you go cheap, figure on lower performance, frequent repairs/replacements, and an overall shorter lifespan of the system.
A few other points to consider.....
When comparing antennas, make sure you are comparing them on the same level ground. If a manufacturer only quotes "dB" on their antenna specs, it's not a complete specification and it's a warning sign. Make sure you compare dBi to dBi, and dBd to dBd. dBi and dBd are NOT the same thing!
Consider lightning protection. It's required by the National Electric Code. It an entirely different discussion than the antenna choice one, so I won't go into it here. If you are going to stick any antenna up in the air, then you need to have some form of lightning protection. Direct lightning strikes are not the only thing you need to be concerned with. Nearby strikes can induce enough energy into your nearby antenna to damage your radio, even start a fire. Even high winds can generate static electricity that needs to be properly dealt with. Any damage by a lightning strike to your home will likely not be covered by homeowners insurance if your installation doesn't meet the National Electric Code.
You can use the highest cost antenna, biggest coaxial cable, but if you do not properly waterproof your outdoor connections, it's all going to get damaged quickly. Water inside your coax cable will wreak havoc with your system. Running a layer of electrical tape around your connections isn't enough. You really need to pay close attention to this. There are some good practices and products out there, but again, that's a topic for another discussion.
Most of all, do it safe. None of this equipment does you any good if you fall, are electrocuted, or otherwise injured during installation.