A good logo and brand is $500 and up. Freelancers charge either and hourly rate or a per-project cost derived from and hourly rate and an estimate of the time a project would take.
You need to check portfolios before hiring. Graphic designers rely heavily on reputation, previous work, and recommendations from former clients. If a designer's portfolio is crap, don't hire them. If they're good, it's going to be pricey but well worth it. In the same way that a good newspaper wouldn't print a story they can't verify, a good designer won't give you a design that doesn't stand up. Those ideas are weeded out well before they make it to you. As a further precaution, we have contracts and typically work with 50% upfront, 50% on completion. This gives you some control as a client while also giving you a reason to see the whole process through.
Most projects will have revisions and that's natural. You're worried about some straw man photoshop hack who wants to rip you off, and that's not most designers. If they have their own website and some decent work in there, they're unlikely to rip you off. The good designers among us want to make something great in this world, not just make a quick buck off of some sucker.
Design contests are trash and you would never get a professional to participate. The line is always that students need experience, but nobody ever mentions that students need experience not only in the work itself, but also in pitching projects, writing proposals, making contracts, client negotiation, and most of all, students need to be compensated for their time like everybody else. If you don't pay someone for the time they spent on the design they made for you, you don't deserve said design. Spec work contests are worthless and so are the people who put them on. If you want a real design, hire a designer. That's what we do for a living.
As for things I wish clients knew, I wish they knew that graphic design is a legitimate business just like yours and deserves to be treated as such. There seems to be an image among clients of a designer that's hard to work with, takes too long, and produces lackluster results when that's simply not the case. We put a lot of time and effort into making you look good and it adds real value to your company.
Just my two cents, but you may want to hire your designer on a retainer after they make your logo. That way you can pay a fair amount per month for design support. Expect that price to go up over time, because that's fair and they're going to end up taking on more and more work.
Bottom line is, you have to pay for design and you're going to have to trust somebody if you want it done right.