I'm a big fan of the Ashford Traveller too, although I have a couple of other wheels. The Traveller is very neat so it takes up little space, is easy to take around in the car, tied into a rear seat belt, and it spins very well.
It is definitely worth trying a few wheels before you settle on one, as preference is a personal thing as in so many areas. Ashford wheels are very functional and plain, but I like that. Other wheels such as Kromskis are very ornate, Louets are ultra modern in their looks. I have a Lendrum Saxony which is beautifully made and so amazing to spin with, but I wouldn't recommend it for a beginner - there is a Lendrum...um...don't know what it's called but it's a castle type; they are very popular, modern looks and have a wheel which slopes. People who spin on them love them dearly, so it would be worth investigating.
For a beginner, Scotch tension is the easiest to manage, and I find a double treadle easier on the legs than a single.
Lazy Kates are sometimes integral as with the Traveller, or they can be free-standing. You will need spare bobbins, carders, a niddy-noddy or two and if you are going to produce yarn in any quantity a ball-winder is helpful.