My question would be best answered by someone who owns/has owned/has played a Behringer GM108

I've been planning on trying to get the GNX4 cuz it looks like exactly what I want, but I just suddenly thought: "Will this sound alright with my amp?" I looked through Manual and saw the page with some basic setting and it has a basic clean setting that effects will come through more strongly; Drive: 6 | Amp: Tweed | Mode: Clean | Speaker: UK | Low: 10 | Mid: 6 | High: 9..... I guess I'd use that, but would this sound ok or would use suggest something else, or should I really think about getting a better amp first?

and I assume the way it would all hook up would be to plug my guitar into the GNX4 and plug that into the amp.
The instructions in the manual are correct. I would suggest getting a better amp. Modeling amps do not tend to take pedals well. The cleanest settings are the only way to go if you use pedals.
ok, and would having the amp on clean and using distortion from the GNX4 work ok? If I remember correctly it had distortion and stuff (goes and looks it up again) I'd really like to get the GNX4 first if it would sound halfway decent and then save up for a good amp so I could have it to play with
If the Gnx is a distortion pedal the distortion on the amp will sound as good or better. Wait and get a different amp (I recommend tube amps) before you start buying pedals. No need to rush out and get a new amp right now, just get familiar with the one you have. When you get ready to upgrade you will have a much better idea of what pedals you need.