No hand held will work with the built in aircraft PTT unless you have some special wiring to re-route the handheld mic audio through the yoke PTT, usually. Some systems may be wired with the mic jack in parallel and work... but don't count on it.
You can get adapters to headsets and put a portable PTT inline with that adapter cable set that will velcro to the yoke if you need it. Usually it's just simpler to hold the radio on your lap and key it with the built in PTT... for the short period of time that you'll actually need it.
As far as the brands/reviews... the Icom and Yaesu are both fine, as is the (very large) Sporty's no-name one. They all have antennas that are removable and adapters are readily available for BNC/SMA/whatever is on the top of them, to feed them into a pre-plumbed connection in the aircraft to an outside antenna (usually by disconnecting the on-board radio from the antenna, or a separate antenna).
Not hooking to an outside antenna, they'll all have limited range. Just the nature of transmitting from inside an aluminum Faraday cage.
The user interfaces are fairly different, none are "great". Recommend getting them from places that will let you return them if the UI doesn't make sense to you.
Rechargeable batteries are great... IF you maintain them. If you're planning on this being a "ride around in the bag until I need it" radio, get a battery pack that allows you to stuff AA batteries in it, and keep a fresh set of AAs buried in the far corner of the flight bag for when you realize the ones in the radio are dead.
Personally, I like the Icom rigs... they're in the same physical case that their commercial HTs are for much harder duty, and I've seen one dropped from an 80' tower and bounce on concrete and still work. If Kenwood made one, like the other commercial radio manufacturer's do, I'd like the Kenwood for UI and audio quality, but they don't. An aviation HT in the Kenwood TH-F6A form factor would be ideal for me.
I also personally HATE the Yaesu UI, which is very similar to the two Yaesu ham radio HT's we own... one is Karen's (she likes it) and one was dad's. They sit unused, and the TH-F6A gets the duty call unless more front-end filtering is necessary, then the pre-buyout GE land-mobile commercial HT's come out to play. None of those are available in the Aviation band...