If you have the designers' portfolios, that's a great start. I presume you've browsed their portfolios and like the general feel of their work -- it should have made you all warm and fuzzy inside and feeling very excited about the prospect of getting them to apply visual magic to your idea -- otherwise you wouldn't have approached them with your site docs in the first place.
Occasionally designers will publish how much they charged for past projects. It's rare, but I've seen it on some portfolios. If they don't publish their per-project fees or normal rates, you might feel comfortable just asking them. Alternatively, you could approach the owners of the other websites made by the designers and ask them questions about what it was like to work with that particular designer, if it was good value for the experience, if they would hire them again, and so on.
That ought to cover you in terms of portfolio and price. Now, as for other things to think about...
Without seeing your website docs I can't comment specifically about the sort of things you'll be requiring, but from your comment above to Randy I presume you've thought it through and have it all sorted out. I think you should talk to your designers and ask specifically how they will approach the project.
Helpful hint: Instead of highlighting the parts of the project that you think will be difficult to execute, see if they can figure that out for themselves based on your project brief and in talking with you. If they do point out the most challenging parts, ask them how they will approach the issues. Do not believe them if they say things like "Oh it'll be easy, don't worry." No. You want to hear concrete ideas -- not necessarily ideas about what the solutions will be, but rather how they typically go about finding solutions (eg through developing personas, A/B testing, testing across all browsers and platforms, thinking about mobile devices, etc.).
Make your decision based on not only their past work and their quoted price, but also how you feel about them as people: are they the sort of people you can talk to about anything related to your website, without any hangups? Do they understand your objectives / business model? Do they ask just as many questions as you do? All these answers should be "yes" to have a good experience with a designer!