Welcome to the forums - thanks for joining!
With relation to the app you're talking about, I am not sure about one that lets you record conversations/turn on the mic remotely, but there are plenty out there that allow you to track your phone, etc.
Have a quick look at the features on
Lookout Mobile - I only have the free version, but the paid version allows a few more features. It is worth noting that, even if you can't get one app that does everything you want, you should be able to get most features you want in a couple of apps. Most apps aren't that expensive... you should only be looking at a few $ each.
As for which phones/carriers would give you the best experience... I can't relaly help with US carriers (I'm in the UK), but I'd definately say get as much Android as you can afford... the experience you get from a high end device is different than that you get from a lower end device. I have a Desire HD and I find Android to be amazing, but my mother in law has a budget device... she only uses it as a phone (for texts and calls), so doesn't think it's bad... I tried to do some (pretty straight forward) stuff with her phone and soon got frustrated. I can't even remember what her phone was, but it wasn't very good.
The best piece of advice is to check out the phones you like in the price range you can afford, narrow it down to a couple (2 or 3) and then get to a shop to get some hands on time with the devices. If you have it narrowed down to 3, you might find that one feels too plasticy, one feels to big (or small) in your hand and one feels just right.
Hope that's been some help to you... feel free to ask more questions if you want more info!
Cheers,
D-U-R-X