Knowing your budget is helpful, or if you have a budget limitation at all….
My choice:
Kenwood dual band mobile radio. D710 will let you do 2 meter and 70 centimeter band, plus it'll support APRS that can be useful.
As for brand choice, it's up to you. This is a hot topic amongst amateurs. Everyone has their own favorite brand, and will fight to the death over it. Your money, you choose.
12 volt 30 amp power supply. More than you need for the above radio, but will support an HF radio down the road if you decide to do that.
Amazon.com: Samlex SEC-1235M Desktop 30A Switching Power Supply, Advanced switch-mode technology, Reliable power with minimum weight and size, Circuit innovations minimize output voltage ripple and RFI: Home Audio & Theater
Stay away from the cheap Chinese stuff.
Dual band base antenna.
Amazon.com: X50A X50 X50-A Diamond Original 144/440 MHz Dual Band Base Antenna - UHF Connector, 5.6 FT
Again, a hot topic. Your money, you choose. Don't skimp on the antenna. Rookie mistake is to buy a fancy radio then go cheap on the antenna. The antenna will make or break your system.
You'll need a mounting bracket for the antenna. That will depend entirely on your home design. No one can tell you want you need unless they see your home.
National Electric Code -requires- a lightning suppressor where the coaxial cable enters the home. No exceptions. A lot of hobbyists will skip this. No skin off my nose, but cutting corners on safety is just plain stupid.
A good lightning arrestor is
PolyPhaser IS-B50LU-CO: Amazon.com: Industrial & Scientific
You'll need to install that where the coaxial cable enters the home. That'll mean you will need two lengths of coaxial cable, one from the antenna to the Polyphaser, one from the Polyphaser to the radio.
You'll need coaxial cable to run from the radio to the antenna. Times-Microwave LMR-400. Not "LMR-400 equivalent". Not "Good as LMR400". Times-Microwave LMR-400 with UHF type connectors on each end. Order the length of cable you need. If you need 20 feet to run from the radio to the antenna, do NOT buy a 100 foot roll of cable and leave it coiled up in the corner. Use just the coaxial cable you need.
You can use other cable, but you need to be aware of the pro's and con's. The type of cable you need will depend on how long the run is. LMR-400 is good for your application and would be suitable for up to around 100 feet or so of cable, but try to design your setup so you use the least amount of cable you can.
The Polyphaser needs to be properly grounded, or it's totally useless. That means a cable run directly down to a ground rod below the antenna, and that ground rod needs to be bonded to your house electrical system. Ideally have a professional do that part. There are a lot of variables regarding conductor size, number of ground rods, how you connect to the house system, etc. That's a whole discussion on it's own.
Once you have it all setup, listen. Listen quite a bit to learn how others in your area use the radio. Don't expect to get an answer the first time you call. Take your time...
You'll get a lot of advice about using digital radios. Digital is becoming popular on amateur radio. Trouble is there are a couple of non-compatible standards. Picking the right one to use will depend entirely on which systems you want to talk on. DMR is very popular, but you'll find D-Star, Fusion and a few others. There are currently no radios that I'm aware of that will do all of them. Analog radio is pretty much standard, and the radio I linked to above will work fine for most of your use. Get some experience, find out what others are using, then make your decision if you want to try digital. I've been using analog only, and have not run into any issues.
The links to Amazon above are only for reference. You can likely find this stuff cheaper at other dealers.