As an artist and contractor there are some things you can look at...
First you need a non-compete agreement and/or non-disclosure agreement.... as a professional artist they would have this available... an artist is a profession and just like a doctor.... you get the practice you pay for. Many freelance artist are licensed for what they do.
I let them know my terms right off the bat so there is no confusion later on...
I charge $100/hr, 50% up front and 50% when completed. There is enough work out there and those rates and terms generally keep me working with other professionals. I have a good demo and portfolio, as well as established client list.
Then I get a general concept from the client for what they want, if they agree to my terms and sign the agreements. I have them sign the agreements because I am not about to work up a concept, then have them have someone else do it for cheaper... works for both parties.
Once we are on the same page with the concept, I quote them how many hours it will take based off the direction and my rates.
Once they agree, they send 50% up front and I get busy.
I send them a few concepts / sketches / storyboards for check off. You do this before you start putting in the main work so they (client) dont change thier mind 3/4 of the way through. Not saying they can't, but if they do it requires you to adjust the price. If you give them the chances to change stuff without charging, they will make a simple logo take 3 months and end up costing you.
Once they approve the concepts, I start on the final drafts. A few more approvals and changes are made.
Once the final product is made, I submit a low res, watermarked version and submit my invoice for the final 50% plus any additional charges.
Legally, as the artist, anything I create is owned by me, intellectual property, until I release it to my customer, therefor I am protected by law and contract.
Once they submit final payment, I send the final artwork, with release papers and thats about it.
Some artist ask for royalties and some dont. I dont really care I just want to get paid for my work.
To answer your question, you get what you pay for.
A good design, by a real artist could cost $1000's. They dont care if its going on a tshirt. Dont give them the schpeel of "oh you can get exposure" or "do this one cheap and I can give you more work".... those phrases are played out and dont work.
I can generally do a nice design/illustration for around $500-$750.... something really nice around $1500-$2000.
I am sure you can find up and coming designers for cheap, but the final product may not be what you are looking for.