Though I haven't done the Money Brook or Cheshire Harbor Trails, I think one of the better first time trails would be the AT from the north. There's a parking area just west of the reservoir, next to some metal building. The AT crosses right there and goes flat for maybe 1/2-3/4 of a mile, then ascends up the northern shoulder of Mt. Prospect. Though it doesn't hit the true summit, there is a nice NW lookout there.
After that, it drops down, crosses the closed auto road, and climbs up Mt. Williams for another nice view (ENE if I recall). It then passes over Mt. Fitch (no real view or marking of the summit, but a few lookouts along the way), past the top of the Thunderbolt, and up to the summit tower (closed).
I did this in November without snow on the ground and it took under 2 hours one way, so its not an overly long hike. The steep sections are the Mt. Prospect and Mt. Williams ascents - you get these done early in the hike. You can bypass climbing Mt. Williams on the descent by taking the Old Summit Road trail (I think that's the name), which starts in the gap between Mt. Fitch and Mt. Williams and dumps out next to the auto road.
The Hopper, as mentioned earlier, is a really nice area too...I haven't actually summitted from this area, but the views from Stony Ledge near it are superb - well worth the 1 mile detour.
The southern approach from the AT is rather long and, though there are some nice views, is a lot of straight out woods trail hiking - not as scenic as other parts of the park.