A1 and Sorcha both have good advice but if you already play other instruments there is one thing you should have learned already: buy the hightest quality instrument you can find even if it's a budget stretcher. The reason is that without a good instrument, you'll hate the sound it makes even if you have the mechanics down. The other reason to buy a top quality instrument is resale. If you find you don't enjoy playing fiddle or don't have the time to devote to it, you can always get your money back out of it, probably with some profit to boot. If you buy a cheap instrument you've wasted both your time and your money.Learn all you can about the construction of violins and what makes one more costly than another. Remember that dealers price their instruments based on craftsmanship, pedigree, and reputation of the maker. The sound the instrument produces has almost no bearing on price; that's assumed to be a mater of taste. An expensive instrument may not have a sound you like and an instrument the dealer might scorn could sound wonderful to your ear.
Take someone with you who is an accomplished player and who has significant experience evaluating and selecting fiddles.
There are still a lot of people with “genuine Stradavarius” violins in the attic. Sometimes you can talk people into selling them for very little money but they're usually not set up to play so you have to have a plan to dump them at a profit should they not pan out. Don't be afraid to dump an instrument you don't like; remember the greater fool theory.
Kenny Baker, one of the very best bluegrass and western swing fiddlers to put bow to string once said he never paid more than $25 for a fiddle and his main instrument is a genuine Steiner.
Good luck,
- Mark