I'm wary of attempts to "spruce up" web apps after the fact. Like skinning desktop apps, often the best you can do is put a pretty picture on a lousy user experience, and generally you don't even get that far. (I was going to go for some metaphor about women and makeup, but I just couldn't make it work: I like my wife best without makeup, but I prefer web pages/apps with tasteful styling.)
Except... I just did this very thing. Or rather, I was the designer. I made a beautiful, humane interface for a web app built by someone who (by his own admission) couldn't design his way out of a paper bag. A rush job, too. Somewhere in the middle when my design looked like blue-gray iphone-rejected ass I kicked myself for taking the job on in the first place, but the next day I pulled out of the blue-gray ass phase and ended up building something I'm really proud of and that the client and everyone who sees it loves. And it was on time and on budget, too (within $50 of the dead middle of my estimate range, in fact).
I'm not sure what the keys to success were in this case. I expect it helped that I was very familiar with the app and its goals, and I think it helped that I'm not (just) a "Designer". I've worked on web apps in almost every technical or creative role, and often I build the whole thing myself from HTTP to pixels.
I don't read news.yc looking for gigs, and frankly I didn't see myself doing jobs like the one I just did--something about not wanting to be labeled a Designer. But if you want to contact me you can use my screen name @ gmail.com.
To answer some of your specific questions:
Legal - Contractor vs. employee & ownership of IP. The first is not hard. Call them a contractor and not an employee (important but not sufficient by itself) and tell them what you need, but don't try to control when or where they do the work (you can have a deadline, but not scheduled hours). The second is not hard either, just make sure you nail it down. The contract I use assigns copyright of completed (and paid-for) Works to the Company but reserves to the Service Provider "(i) know-how, techniques or general expertise used and/or developed by Service Provider in the course of providing Services hereunder; (ii) pre-existing materials or intellectual property; (iii) all generally known or published information; or (iv) other software and related ideas, designs and materials which Service Provider has developed or is developing for itself and for third parties" while granting to Company a limited license for any of the above insofar as it's incorporated into the Works.
Deliverables - You should receive working HTML files with all the accompanying CSS, JavaScript and images, but also the PSDs or whatever that went into making them. @brianr, "slices" are for tables and CSS designs that wish they were tables. No one can provide you with the images pre cut correctly without knowing exactly how the page will be built, which no one can know until it's built, because if there's anything technically interesting at all about the CSS, the first implementation is likely to have some issue in some browser.
A PSD is not enough because a webpage is not (unlike a magazine page) a static image. It's especially ludicrous to consider a PSD much more than a concept when you're talking about a web app (i.e., a collection of web pages where many pieces are not only dynamic but functional).
Price - second NoBSWebDesign that this is really impossible to even ballpark without knowing a lot more about your app and what you need. Personally I don't take jobs for a few hundred for people I don't already have a relationship with--too much overhead. OTOH, I recently had a subcontractor do a really nice design concept for me for a simple professional site for less than $200. But that was only to the PSD stage (a concept that still needed to be brought to life in code and web graphics) and with a lot of guidance from me. And it was just a small professional website, not an app.