For the final conversion to POF (by any method), you should try to have as few separate objects as possible both for efficiency and stability reasons. So, in your model there, you'd end up with:
Fighter
|
|-Wings
|
|-Cannons
as a final hierarchy, but for no real reason unless you want to animate the wings and cannons in some way.
As for programs, I would really really really strongly recommend against using TS 3.2 (AT ALL) due to its overall instability, complete lack of good modeling tools, horrificly clunky interface and terrible work-flow, and that instead you should go for either Maya or Blender.
Blender has the (pretty big IMHO) advantage of having a direct conversion path to POF via saving as DAE (There's a guide on how to do that
here), as well as being very capable of any animations (effects, cutscenes, head ANIs, command briefing ANIs etc) that you might want/need, it's free and continually evolving.
Maya has the advantage of being a very powerful mainstream program used in professional CGI work, so it's *probably* more capable than Blender for the non-ship-building applications. (I've not used it myself, so I can't really give much more info sorry - I don't know if it can save to DAE)
About texturing, well there is a lot to learn there, but essentially it comes down to tile mapping or UV mapping. I
loathe texture tiling, so I'd actually recommend you learn to UV map from the get go, but for beginners tiling might be an 'ok' way to get a grasp of the concepts before you get comfortable enough with the modelling side to work out the ins and outs of how it relates to the texturing side. It might be better to pick a modelling program and focus on learning to model well before tackling texturing (in that same app - don't switch for something like lithunwrap). Learning both modelling and texturing at once might be pretty overwhelming.
For texture painting you should be able to use just about anything that's not MS Paint, but the big 3 would be Gimp, Photoshop and Paint Shop Pro. I currently use PSP, but I plan on switching to PS because my version of PSP does a lot of things that piss me off no end, like taking ages to save auto-saves, and then not actually being able to restore them when it crashes. :\
Finally, don't be afraid to put pen to paper when coming up with ship designs - just rough scribbles of interesting shapes/outlines are infinitely better than making up a shape as you go in a modeller, only to find it looks ridiculus or simplistic at the end of it.