I would figure out the range of salary the type of position usually goes for, then start with an estimate slightly higher than that. Assuming this a full-time role, you'll need to account for things like "office" expenses, healthcare, utilities (internet?), and what you will eventually owe in taxes. Contractors' rates will often be "higher" than salaries for the same position because of this, but in the end the amount you actually take home will balance out.
I've done contract work since finishing university, and managing taxes and expenses has been a constant challenge. Make sure you're comfortable with the deal you make.
I've had success combining these two ideas: my desktop has a separate user for work, and I'll access it through SSH or a remote desktop from anywhere with my old Thinkpad. Using this setup at the library really helps me focus, for example.
The laptop (a Thinkpad X201) I picked up off of ebay for $100 or so too, so it's a decent option if you don't want to spend extra on a high-spec laptop.