Lots of good, quality beginner stretches on our rivers here....
On the Gunnison...the "upper" runs from Almont to North Bridge (Garlic Mike's) and is flatwater cruising with optional features that is more suited to fishing. Its II, II+ at best in spots.
the "middle" is from North Bridge to the WW Park and is mostly flat with a few sections of rollers and wave trains. Again, class II most of the way.
the "lower" is from the park to McCabes Lane west of town and is the standard town run for Gunny locals. Its a full step above the rest of the runs, with the whitewater park and a three-stage diverson structure coming at you within the first 1/3 mi. there is a long II+ rapid at the bottom, this stretch rates at least a II+/III-.
On the Taylor, it gets harder as you go up. The easiest stretch is the Lower, which starts at Fivemile and goes to Almont. There are a few straightforward rapids at the top but it mellows out quickly. Its easy but it requires paying attention to dodge the cosntant supply of rocks.
The middle, upper, and upper upper taylor are all more intermediate with endless class III boulder gardens and wave trains, and a few III+ technical rapids thrown in.
The bottom four/five miles of the East are floatable but does not contain much beyond flatwater floating, best suited to fishing.
The Lake Fork has a couple of decent beginner stretches on it, the Box being the best. its 11 mi and is mostly class II with a few III moves.
Check out Kayaking Information
for some more detailed info, hope this is a good start