Well, I didn't really have to think much about which style of guitar I was going to build. I had always wanted a Strat, and this is what I was going to make. Now if
you ever decide to build your own guitar, and you really don't mind which style you want, then I'd say doing a Telecaster or maybe some sort of customised Les Paul Junior design would be much, much easier. Why? because there is no tremolo to think about, and you don't have to carve out all those contoured bits around the Strat's body.
Fender Telecaster
Gibson Les Paul Junior
That said, a Strat design is by no means the hardest either. Let's take a Les Paul Standard as an example. You'd have to think about a fixed neck (difficult to attach, with very little forgiveness if you make a mistake), sculpted quilted maple top (a lot of work, and easy to mess up), body binding (also a lot of work, and a whole art in itself), etc.
Gibson Les Paul
So here's my list of things to think about, and what I recommend for the easiest option:
1. Neck attachment - recommend bolt-on neck
2. Body top shape - recommend flat (slab) shape
3. Knob and pickup mounting - I would say that mounting all of these on a scratchplate is more forgiving if you stuff up some of the routing.
4. Jack socket placement - You can either mount this on the edge of the guitar (like on a Les Paul), on the face of the guitar, but not within any sort of scratchplate (like most Fender Telecasters), or on some sort of scratchplate (like, say, a vintage Hofner Colorama).
Hofner Colorama
5. Tremolo/vibrato - Easier to give this a miss, although if you decide to go for it, think about a Bigsby-style unit, which can be mounted on the top of the guitar without the need for any routing.
Bigsby tremolo/vibrato
6. If no tremolo, think about if the strings will go through the body (like a Hardtail Stratocaster) or not (like a Les Paul). Not going through the body is the easier option.
If I were to repeat this whole adventure again, I would have a slab body, with no sculpting/contours, a scratchplate for the controls and pickups (possibly the jack socket too) and a Bigsby tremolo.
However, at the time I did this, I had it in my mind to do a Strat, so that's what I needed to plan for.