Turbodime - first thing to say is a big welcome to the forum.
There is going to be no perfect antenna for your application - antennas designed to work across such a large bandwidth (i.e. 155Mhz - 855Mhz) are compromises: they'll be just above/below resonance i.e. tuned) for a small part of the 700Mhz spectrum they operate over. That "close to resonant" bandwidth will be 50Mhz - 150Mhz of the overall bandwidth of 700Mhz and is going to fall into (even though it is coiled), I'd "guesstimate"off the top of my head - and is going to be in the upper half of the overall 700Mhz.
So - first question (at least what I'd be asking myself in your situation): what is the range of freqs used most by the poachers, or, in what part of the 155Mhz - 855Mhz spectrum would you like your antenna to work best in e.g. between, say, 300Mhz - 500Mhz, or between, say, 400Mhz - 650Mhz?
With that question in mind, or even better, answered, go out and search for an antenna for handheld use - but another one (or 2) for use in the car - and there is going 2b literally 100's of options on the market.
There is also the issue of rf filters (e.g. band pass) and pre-amps - and with handhelds, the correct choice of & implementation of these components can add substantial real world performance gains to your scanner/receiver (emphasize on the words: correct choice, implementation & real world*) - otherwise they can be:
a) a waste of money
b) can downgrade performance.
* Read "real world" gains/improvements as I wrote above, as improvements you are going to experience & hear.
Moving on use of the handheld in the car: first thing - you've got a decent bracket to mount it onto(?) - if not get one.
As far as antenna(s) choice goes - how longs a piece of string?
In your situation I'd be designing and constructing an antenna, but that's what I do in as an electrical engineer - I spent my life designing them - easier for most folk buy them, and nothing wrong with so long as to have some basic background knowledge to help you arrive at a sound choice, and/or a shop assistant who has the knowledge, and is willing to advice you & give you the time you need as a customer to chew over the options.
I think you should split the 700Mhz spectrum you wish to monitor into 2: choose an 1 antenna for +/- 150Mhz - +/-500Mhz and a 2nd for +/-500Mhz - 850Mhz. Have +/-10% over-lap at between the 2 antennas at 500Mhz.
If funds permit, add a 150Mhz - 500Mhz band pass filter to the lower band antenna and a 500Mhz - 850Mhz filter to the upper band. Not going to get into "filter theory & detail" unless you specifically want, but if you do use them a low-ish gain preamp added on to each antenna side (after the the filters) would do no harm.
How to connect them up to the GRE? - through a decent quality splitter/combiner (S/C) S/C's are great components, but they can totally mess up RF performance if not chosen and setup correctly
The points in the manufacturers literature to examine when selecting an S/C are INSERTION LOSS (read up about it on web) and PHASE MATCH/MISMATCH (again, read up about this on the web - as close to 0degrees as poss, especially in the overlap region) and
As far as antenna brand/manufacturer goes, and yes, I know that was your question, I wouldn't have a clue. There are so many manufacturers out there who make decent quality hardware, and many who make crap quality gear. I wouldn't be too concerned about rand name, but more so about the hardware been:
a) in my budget range, and just as important (if not more so)
b) having good electrical/RF performance characteristics.
So sorry I haven't said, " use this or use that" (to start with I'm UK based so the gear we have out here may not be available on the other side of the pond), but I've shared with you an opinion (mine, for what it worth!), and some background theory that will help you come to some decent good decisions when selecting the gear to use to get the most out of your project.
All the best, and by all means feel free to ask as many questions as you want - the forum is full of folk more than willing to to share their experience/s and knowledge.
