I certainly agree with Mav, Kathy, and WD regarding the important complexities and safety considerations for Sierran mountaineering and scrambling.
As for climbs to get one accustomed to steep class 2 route finding/class 3 scrambling and exposure, here are a few enjoyable ones I can think of.
1. Mt Conness, particularly if going from Saddlebag lake over the top of 11239. If done correctly, using the S. side of the E. ridge this is pretty much all class 2, with the famed and somewhat exposed "engineered" final knife edge moves. This involves fairly open (good line-of-sight) route finding to pick some nice benches on the S. side of the E. ridge, then surmount the top to to join the crest (rated 3rd class in some books, but really just steep 2nd). The summit moves at the head of the S. ridge are fairly obvious owing to the engineering of the trail and the fact that there is really no other way to do it without it becoming truly technical. It is here that many beginners find out what their tolerance (or lack of tolerance) to exposure is all about. I have seen some folks turn around at the base of the knife edge section. All in all, I think this is a really fun easy mountaineering route on a really attractive mountain. The other positive here, is that there are no real "preliminaries" one is nearly scrambling right out of the car up the side of 11239 above Saddlebag (easier and more fun to do this than sidehill around it to save elevation loss, in my opinion).
2. Tower Peak. This is a truly beautiful mountain that can be seen from everywhere and has a nice rugged appearance. The only drawback here is that is a fairly long hike to the start of the standard route from the pass to the north of the peak (from Tower Lake). From a distance, the route looks very steep and worse than class 3, but when you get into the gully you find that the ledges are really wide and that this is really a very steep class 2 climb rather than class 3.
3. I agree with WD's pick of Agassiz. It's a beautiful peak with an exceptional view. It is class 2, but you have some choices in terms of doing some low 3rd on spurs to avoid loose rocks on the ascent versus choosing to stay in the looser class 2 chutes to aid your descent. This is good practice for beginning route finding strategy.