Like MJC has already said, both of the vises you mentioned are good ones. The Dyna Kings have one of the strongest jaws with very tenacious hook holding in the business, and they are made out of quality machined metals. The Danvise has a very good jaw with good hook holding, but is is not made entirely of machined metal. Some of the Dan Vise parts are very hard and durable modern plastics; it is an excellent vise though. Anyone who knows me or who has been around the forum a while knows I use a Dyna King Barracuda and that I think it is the best vise on the market; but it is not a vise I recommend to beginners.
Regarding the Danvise and Dyna King Kingfisher, I'd take the Kingfisher because it has a better jaw and will literally last a lifetime.
MJC also mentioned the real heart of what you need to be looking at in a vise. The key is not whether a vise is rotary or not, unless you are going to be tying rotary or looking for a vise to tie married classic altlantic salmon flies, or involved saltwater flies.
There are several very good vises on the market that are not rotary, but I strongly suspect the non-rotary would be a better choice for you, especially since you are a brand new, beginning tyer. The simpler the better for new tyers.
Griffin has several very good vises under $100.00 and there is always the venerable Thompson Model A (which has been put back into production since someone stepped up and bought the old Thompson Vise Co., thus keeping this fine, lower-priced vise in production).
MJC's generous offer to let you test drive a few vises is something you should seriously consider doing. This way you can make a purchase on the basis of which one you like.
One thing I would caution you not to do is buying a fly tying kit. Kits are full of stuff you won't use, have generally poor quality materials, generally have poor quality tools, and are a poor buy. You are far better off getting a good vise, good scissors (good ones are between $10.00 and $35.00), a good bobbin (good ones run $6.00 for the S&M to around $20.00 for the ceramic ones), and a Materelli whip finish tool.
Buy materials and hooks in 2 or maybe 3 sizes to tie 2 or at most 3 of the flies you will use to start out with. In the long run, doing this will save you a lot of headaches and actually cost less than having inferior materials and a bunch of useless stuff. After you get the 2 or 3 flies down pretty well, add the materials for another fly or two. Continue doing it this way and you will never get stuck with materials you won't use.