Hi, welcome to the forum. There have actually been a few similar queries to yours quite recently, so you should have a look around to check some other answers.
Graphics cards: Picasso IV and CyberVisionPPC seem to be very popular, though there are others. These two are probably the most expensive. You should also have a look at flicker fixers/scan doublers. If you can't get one of these built in to your graphics card, you will probably want one to display native 15kHz screen modes on your SVGA monitor.
For gaming, check out WHDLoad, to install games onto hard drives. The 1200 can handle pre-AGA graphics, but I think some games may look for older ROM versions. If you are using Workbench 3.5, you will need 3.1 ROMs. I think a lot of older games, which are still very good and popular, were written for 1.3 ROMs, or others. I believe WHDLoad avoids that problem, as well as having all the games conveniently located on a hard drive. There are also options for loading different types of ROMs into memory, which may be OK if you can't use some particular game with WHDLoad.
As far as internet usage is concerned, many people are happy with broadband connections with 10Mbps ethernet cards, at least as far as downloads, email, ftp, IRC, etc are concerned. However, web browsers are not Amiga's strong point. Also, if you want to look at content such as movie previews online, you will probably end up doing so on your PC. Generally, Amiga browsers are not updated frequently enough to maintain compatibility with current protocols and content. This is unfortunate, but it's a small market on aging hardware, afterall. The 1200 has a PCMCIA (I think version 1, or 1.1, but not version 2) slot, which can take older notebook ethernet cards. This is a really convenient feature, as they are cheap, and plentiful, secondhand.
As far as 'new AV features' go, remember that these are classic machines, and will not generally compete with comparably priced PC's. There are PCI expansion boards available, which can take Voodoo 5's etc, but I haven't used them and can't comment on their capabilities. I believe there are some software compatibility issues. Amiga's used to be leading the AV field, but that was some time ago. People still use A4000's as video workstations though, and I think one person on the forum also uses a CD32 running SCALA to do video jockying in clubs, etc. He is very pleased with the capabilities of his system.
If you want to replace a PC completely, I would suggest a PPC/060 accellerator, and the best graphics card you can get. Otherwise, performance and features will probably dissapoint you.
Something else worth playing with is WinUAE. The current version is an excellent emulator of the classic Amiga hardware. You will need a copy of ROM files and Workbench disks to use this though.
The highly modified classic Amigas are still capable of pretty impressive tasks, and a lot of people enjoy using them. If you can't afford to expand a system heavily, I expect you probably will end up still using your PC for a number of duties.
Have fun, and see you round the forums,
Oli
