I'm a bit stuck on what to do now. If I mod the game, I won't be allowed to play it online. I don't really want two installations.
It depends what you mean by "mod". I really can't see how changing a few textures would harm it, however changing shapes of landscapes and cars probably will. You might be safe with cars, providing you don't change the length of cars hugely (e.g don't replace a blista compact with a limo). If you crash, though, you're screwed. The person you crash into will see your car as a different size to what you do. It could go either way, really. It might just look odd for you, but be fine for everyone else. Who knows.
But yeah, changing colours or textures won't hurt. Just don't change the shape of anything.
For those of you who do mod the game, here's a few great sites you may not have come across, and a few you probably will have.
GTAGaming.com - Does what it says on the tin. There's a nice supply of items, but it hasn't been updated for ages. Probably won't be either...
GTA-Mania.com - An impressive french site with a wide variety of mods and cars. Don't be put off by the language difference - although the readme files don't make sense, they've still got all the details you need. Places like GTA Gaming pass up the huge number of french models just because they can't be bothered to re-write the info files.
Grandtheftauto.fr - Another french site with an impressive lineup. This place also arranges their vehicles by the cars they replace and the type of transport, which is handy when you can't think of a good replacement for something.
Sanandreas-fr.net - Yep, more french sites...
GTA-worldmods.de - German, this time. Looks like there's a wide variety of mods around, so it's worth a look.
If you want more, try a different method to searching for them: instead of sticking in "GTA mods", search google images for some cars that are BOUND to be available for it (e.g Chevrolet Caprice cop cars). You'll get pictures of cars in gta, which link you to these kinda sites. Or try stuff like gta garage mod manager. I picked up the last one in the list from doing that.
Anyways, enjoy modding!