1) There's a way to get nearly, if not every single OCS game to run on a ECS or AGA machine. Many of them will just boot up without any problems, some require you to switch to OCS mode from the Early Startup Menu (by holding down both mouse buttons when you switch on or reboot the Amiga), by using a degrader disk which will set up the memory and load a 1.3 Kickstart into RAM, or the best way is simply to use the amazing WHDLoad, which allows you to install all your old favourites to your hard drive, play them and quit back to Workbench without ever needing to reboot. So don't let those old incompatibility problems scare you off, we overcome those years ago!
2) AmigaE is an excellent language to learn for the Amiga. It's easier than C and compiles faster, yet is just as powerful, and allows you to use inline Assembly for when you want to hit the hardware. The compiler is free, and if you decide on it I can help you to find documentation, and we have an IRC channel on FreeNode (#AmigaE). Of course you could still use C, Basic (Amos, Blitz, or HiSoft), or 68k Assembler if you are dedicated. I'll let other people suggest their language of choice, but after much consideration when I was deciding on a language to learn, I settled on AmigaE because it's very well suited to the Amiga OS and is capable of creating powerful and efficient, professional quality software as well as games.
If you just want to make games quickly, there are several dedicated game maker programs for various genres including Text Adventures, Shoot 'em Ups, Platformers, and Point & Click Adventures.
3) As long as those floppies aren't dirty or full of mould, they might still work, and can be formatted as 880k. If your Amiga is a later model A1200 it might have a modified PC HD drive in it, which won't read HD floppies but will require you to put tape over the extra hole on all your disks or it won't recognise them. Using HD disks formatted as DD isn't very reliable, they develop read errors pretty soon. If they're just games, written from an ADF file, usually all you need to do is write the image back to the disk and it will work again (I always write an ADF twice or three times in a row to make sure it's really stamped in there). Just don't use them for important storage.
4) I recommend an A1200 or an A600. They both have IDE and PCMCIA which is very handy, allowing you to use cheap CF/SD card adapters and network cards. Stick Kickstart 3.1 ROMs in it, a 4-8GB CF drive, and look for either a second hand RAM card or accelerator, or purchase one of the new ACA accelerators from Individual Computers.
Check out YouTube to see lots of cool stuff people are using their Amigas for, I use my A1200 every day as my main computer, and use several other Amigas and Amiga-like OSs on various hardware, and I'm going to try and upload more videos as I get the free time to make them. Here's my channel anyway:
http://www.youtube.com/user/AmigaCammy#p/uOf course there's nothing wrong with having more than one Amiga, so if you can get an A500 cheap they're still really cool retro machines, and you can use them to test the games you make for A500 compatibility (since it's a common target configuration for Amiga games developers).