Researching pay ranges
Our grads in both the Seattle and Portland areas generally have salaries between $45-60k to start. Glassdoor.com is a great resource for researching salary ranges for different types of positions, as well as for roles at specific companies. If your technical skills are on the weaker side, you're interviewing for a job with tools or languages you haven't used before, and/or you don't have much professional experience, you'll probably make on the lower end of this spectrum, or even below; if you are very strong technically and have at least a few years of professional experience, you'll probably make on the higher end of this. You can use these numbers as a starting point, and even share them with prospective employers as appropriate.
These numbers are not absolutes, by any means! Some students who were middle of the pack in their technical skills and with only a bit of professional experience have ended up on the high end of these figures because they really hit it off with a manager at a company. Other students who were very strong technically but had weaker interview skills have started out with salaries on the lower end of this range.
Calculating hourly contractor pay
The first thing to think about is how long the project will take you. If you can estimate the number of hours, then that will give you a sense for what the hourly pay breakdown will be, and if the amount they've proposed is adequate. These resources have some good info on calculating your hourly contractor pay:
For contract work as a freelancer, a typical rule of thumb is to charge 2-3x what your hourly salary would be otherwise, to account for having to find clients and downtime between projects. But in a contract-to-hire situation, usually the premium is lower, since if all goes well, you won't have to find another client or have downtime. You still want to add in something to account for taxes, benefits, sick days, vacation, as well as the risk of being a contractor vs. an employee, so you might take your expected salary and add 30-50%. Since our grads generally have salaries between $45-60k to start, you could work off the percentages for those numbers. These are by no means hard and fast guidelines, but should give you a sense of where to start when calculating whether the payment they quoted for the project is feasible for you.
Crafting a counter offer
It's perfectly acceptable to come back with a counter offer, and it's pretty uncommon for an employer to rescind their offer because a candidate tried to negotiate. When negotiating it's usually a good rule of thumb to ask for around 5k above what you'd be willing to settle at, with the hopes that they'll be able to meet you somewhere in the middle.
You could format an email to them along the lines of:
Hi hiring person,
Thank you very much for extending this offer, and I'm excited about the prospect of working for your company. I'd like to talk with you a bit further about the salary you've offered, and discuss the possibility of starting closer to X amount. List reasons why you'd like to be making closer to that amount/give some compelling reasons for them to consider it
Thank them for their consideration, and that you look forward to hearing from them
Bottom line: make sure you orient your wording towards acknowledging you'd like to work together to find a salary that will be mutually beneficial.