I think the tommie is a great trainer (if you learn in one, you'll have no problem flying most other tricycle singles), but as I did both PPL & IMC in one, I'm unashamedly biased.
Your plan is sound, but finding one that isn't by now well work & tatty might be a challenge. Wing life limits & some parts cost/availability (noselegs?) mean many have been unloved for awhile now.
Once you've got your PPL, a cherokee would likely be a more useful & versatile aircraft; you could buy an early 140 now, but IMO they're too easy to fly to be an ideal trainer.
In an ideal world, I'd say train in someone else's PA38, then go buy a PA28 - the transition is trivially easy.