My project is in an early stage where it's just three of us building the product and not spending any money on things like IP lawyers.
We have a domain name that is very good, though, and it's important to trademark our name so that we don't face any legal challenges to the URL from someone holding a similar trademark.
What do you think? Is this something we can do on our own?
Learn the difference between (TM) and (R) --The former is you claiming use of a trademark and the latter is having a formally registered trademark.
Anyone can claim use of a mark (TM), but getting a real registered trademark (R) requires jumping through all of the correct hoops (forms/fees), and someone at USPTO validating your claims.
There's often some confusing language about 'use' of your mark in commerce. If a mark is not used/maintained, it is abandoned. Similarly, you ought to be using the mark to get it registered.
Many companies make very questionable (nearly fraudulent) trademark claims with (TM) designations that would obviously NEVER be approved by the USPTO. I classic example is Intel claiming a trademark (TM) on the word "Core" when it has been in common use in the specific area of commerce (class) for a long time before Intel started asserting the bogus claim.
If you do some digging and studying, you'll find getting a registered trademark is really fairly simple.