Crystal, you mentioned Scottish fiddling and since that's the style I've been concentrating on for the last few years, after initially learning classical violin, then Irish fiddling off and on for a few years, I thought I'd respond.
Regarding positions, it seems one can do quite well in Irish fiddling without ever going above 1st position, but in Scottish fiddling 2nd and 3rd positions are useful (however you can still probably play most the tunes without going out of 1st, particularly if you can extend your 4th finger like Simon mentioned). Coming from a classical background, one thing I found interesting was that a lot of the Scottish fiddlers didn't use 2nd position at all; it's either 1st or 3rd. I've found 2nd position a handy thing to have in my bag of tricks, though if I was just starting out and didn't intend to ever play classical music I don't think I'd put the time into learning it.
What to work on next? For Scottish fiddling I'd say left hand work on ornamentation like grace notes, crans or rolls, double stops, etc., plus general intonation (and positions, if you decide to learn them); and right hand work on the various bowing techniques (snap bowing, stutters, and so forth). What I'd also concentrate on is getting tunes up to speed. I recently started playing for dancers and I found that a lot of the tunes I thought I knew pretty well are a lot scarier when you need to play them at dancing tempo without making any mistakes! If you're intending to play in a tradition that doesn't condemn playing from sheet music (playing for Scottish country dancing, it's quite common to play from sheet music, but try that at a session and you'll get laughed out the door, or at least looked at funny) then I think working on sight reading skills would be helpful. It never hurts to memorize tunes (but I think that's probably something you would work on yourself, without a teacher's help). Anyway, I hope some of this rambling is helpful! Good luck -Steve