Do a little Google searching about where to look for gold in rivers in colorado. There is a great forum out there but I can't remember the name. I think it is treasurenet.com.
There is a colorado section there and the guys are VERY helpful.
As far as the trout thing goes, I would check. Don't want the trout being disturbed and have a warden fine ya.
Regarding the old timers already taking the good stuff... There is plenty still around everywhere.! I still get some good flakes out of clear creek right in Golden. Even in the town of golden. Just have to avoid the obnoxious and annoying kayaks. They are RUDE, obnoxious, and will do everything to get in your way or totally paddle through your setup. This happens often right in the town of golden on the river. They gold prospectors call them Yackers and have some fun stories.
Before you decide on the expense and bulk of a dredge, get a pan or 2, a bucket and shovel and have at it. Read a lot about where on rivers to prospect and proper panning skills. Panning is still used even when you have a dredge. It's a very important skill to have or you will waste a ton of time.