Hi The Hairy Log Book, top of the morning to you!
The Traumahawk was built as a result of a survey to some 10,000 fright instructors. It is, in theory, everything that a flying instructor wanted from a training aircraft. It has a great big cockpit perspex canopy which offers excellent visibility, a small wing, a very easy fuel management system (with the selector and gauges right in your face on the fuel quadrant), it has docile (yet very responsive and firm) handling characteristics, reasonable performance both as a trainer and tourer, and very low maintenance costs. It also offers a predictable student performance when stepping up into the Piper big brothers.
The one concern that I personally have with the aircraft is that the production aeroplane was not the aircraft that was initially certified in Vero Beach, Florida! Test pilots who flew the PA38 saw the production aircraft roll off the production line and couldn't even identify it. The wing design had changed with a reduction in the number of spars to decrease weight, the tail had undergone modifications and numerous other cosmetic changes were evident. The FAA published a story a few years ago entitled "Tomahawk on Trial" which questioned Pipers motives and brought to light the changes that were made. If I find this story I'll post a link to it. It's really interesting reading.
Having said that, the Tomahawk has proven itself over time to be reliable and safe. The test of time is more revealing than any period of test flying.
I used to teach spinning in the aircraft until quite recently when I came to the conclusion (after a flat spin in the PA38) that the only aircraft worth spinning were ones certified for aerobatics. This stands for the skipper as well.
The Skipper was designed (in response) by Beechcraft to compete with the PA38 and the flooded market of decrepit old 152s. It was designed and modelled on the PA38 (by the same designer) who ensured that the manufacturer actually built the aircraft he put on paper.
I personally find the Skipper boring. It lacks the same 'feel' of the Tomahawk. It is noticeably slower and although it offers the student the logical progression onto bigger Beech aircraft they aren't nearly as common as the Piper types.
Having rambled all that...the aircraft are much-of-a-muchness at your level. You probably wouldn't be able to feel the subtle differences. The aircraft type really shouldn't be a consideration.
The only aircraft I would suggest you steer well clear of is the Cessna 152. Although it's the most popular trainer ever built, I feel this is only because of lack of options over time rather than the appeal of the machine. It is slow and sluggish, it is not responsive and it offers disgracefully poor visibility in all phases of flight. The 152 is also small and cramped (even for two small people), has generally poor performance and it is as ugly!!
Go with the school that you feel more comfortable with. Fly with the instructor that you feel will give you more personal attention. Try and do your training with a company that operates larger commercial aircraft and can give you some commercial exposure on the completion of your licence. If you're doing a CPL, make sure that your instructor has significant commercial experience himself. There are far more important questions than aircraft type.
Good luck!
T.