Yes, the Amiga 1200 is a wise decision. An Amiga 4000 would be ideal but much more expensive.
You can get a stock one at several Amiga stores (check the links of this sites) and Ebay.
The best possible upgrade that you can make is an accelerator card with some extra ram on it. The built-in CPU is too slow and the memory too low for anything serious.
This will help you greately to connect to the internet. Web browsing will be limited to 256 colors, of course, so you may want to add a graphics card as a next upgrade.