Most of your initial training will be done in one type of aircraft, though this isn’t universal, but you’ve got enough going on that you don’t need to worry about the differences between aircraft.
The majority of flight schools in the US will start you in a Piper Warrior or Archer, a Cessna 172, or a Diamond DV-20 (sometimes DA-40s). Smaller schools might have a 152 (the larger schools also use them for CFI spin training). We’re starting to see the new Piper Pilot 100i hit some schools.
Some are going with light sport aircraft (LSAs) like the Sling, maybe a Cessna Skycatcher.
After you earn a private certificate, it’s a progression. If you’re learning complex aircraft (perhaps for a commercial certificate), that’ll often be done in a Piper Arrow, sometimes a Comanche or a Bonanza.
Other non-complex commercial training might be in a 182 or Cirrus SR-20/22, but might also stick with 172, PA28s or Diamonds, depending. Any of the above can be used for instrument training, if properly equipped.
For multi-engine training, these days it’s often in Piper PA-44 Seminoles. Occasionally you’ll see a Piper PA-34 Seneca or Beechcraft B58 Baron, maybe less of a chance they’ll have a Cessna 310 or a Beechcraft Duchess, but those are getting long in the tooth.
This doesn’t account for a lot of independent FBOs/CFIs who have a wide range of aircraft, or the owner/student who brings their own.
If you’re willing to do the progression and not looking to skip too far ahead, I’d suggest getting the JustFlight Arrow series and the Carenado Archer II. Heavily recommend the JPLogistics and WBSim mods for the stock 172 and 152. Almost every other aircraft I mentioned above is available in one way or another except the Skycatcher, Piper 100i, Duchess, and the Comanche, though that last one should be coming soon.
And as far as steam gauge vs G1000 - most flight schools are going toward the latter. I think it’s good to learn both as the skills complement each other nicely, but there’s obviously a lot more knowledge that goes into operating the G1000 correctly. That said, during your primary training, you’re mostly taught to get your eyes off of the instruments except to verify and cross-check that it’s doing what you want it to be doing. Eyes outside with short glances inside.
Hope that helps!