You can't go wrong with Dyna-King, Renzetti or Regal. The Renzetti Traveler or the Presentation 2000 are lifetime vises that will handle almost anything you want to tie. The same goes for the Dyna-King vises. I have had good luck with the Dyna-King Barracuda or the Dyna-King Barracuda Junior Trekker. You also can purchase a midge jaw for both the Dyna-King vises. The standard Barracuda vise is more money; the Trekker is smaller and less expensive, but still a lifetime vise. I would order midge jaws if you plan to tie primarily very small flies.
One choice you will have to make is whether you want a desk top (pedestal) or c-clamp model. I have both, but always try to use the clamp-on model because the c-clamp connection to the table is more stable. The c-clamp also gives your more height adjustability for using it on different table tops. The pedestal base will fit on any table top, however the tying ergonomics may suck due to the height of the table. If you plan to use your vise a lot, you may want to consider the ergonomics of your set up. C-clamp bases allow for more adjustability and you can adjust the height of your vise to the most comfortable and ergonomic position.
If you don't want a rotary vise, the non-rotary Dyna-Kings retail for less than $200. Be certain to avoid the Regal knock-offs made offshore. One of my fishing partners purchased one by mistake and had the jaws shatter after a year's use.
Some of the advice you get about vises will be based on personal preferrences. For example, I have used a Regal vise before and found that the vise got in the way of my left hand. The relatively straight design got in the way of how I used my left hand when tying. Admittedly, I was just using the Regal temporarily and didn't have the muscle memory/practice on the vise where it's use was automatic and worked for the way I tie. Other tyers I know swear by their Regals.
For what it's worth, I would purchase a rotary vise because it gives you the option of both rotary or fixed operation. Whatever you decide, buy the best vise you can afford from a reputable fly shop and you will have a lifetime fly tying tool.
Good luck with your decision and welcome to the world of fly tying