Definitley PA28 ..... I flew both during my training and the PA28 is certainly a much friendlier aircraft to fly than its PA38 relation. If you can afford it, go PA28, it will teach you how to land properly as well, because the flare will seem to go on for ever during the early stages of your landing training. QXC's are also much less stressful since the PA28 is a very stable aircraft unlike the PA38 which constantly twitches about. 8-)
Aussie Andy I must correct you on one important point :
re: PA38 faster .... Andy, the PA28 is faster, its a bigger aircraft with a bigger engine, it climbs at 79 IAS, descends at 70 IAS and cruises happily at 100 IAS (or even a little more). The PA38 (if memory serves) will only climb at 70 IAS, descend at 70 IAS and is much happier cruising around 90 or 95 at a push. Your account of "the other guy" could be influenced by many factors, and you have not taken these into account from what I can tell.
The PA28 is great, especially at the later stages of the course. However, if you do train on a PA28, I would strongly advise everyone to get their instructor to take them for a SSAT lesson in a PA38, it is useful to see how different aircraft react.
TTFN