Call your DMV and the DMV for the state where you're buying and just ask. Here in PA, we can go to the DMV but it's super easy to use a DMV notary service. Every town has multiple. Quick, easy, no brainer.
Every state has different requirements for notarization. You need to follow the rules based on the most restrictive set of rules. For instance, in PA we require notary. TX does not (or at least it didn't when I lived there). I could fly to TX, the seller could sign the title, and I drive home and register/title the car in PA. If the source state DOES require a notary, I have to have the title notarized there before I return.
When it comes to legally driving the car, there are multiple ways of doing it. The first way is legal, but sketchy, but it can be made less sketchy. Ask the seller to leave their plates on it and you agree to ship them back after your trip. This can be an issue for the seller and many don't like to do that. If you (for instance) blast through a speed camera, take a toll road that logs the plates, or use the car to rob a bank, it could mean loads of trouble for the seller. In most situations a bill of sale will indemnify the seller from those charges. It's totally just as legal as if you borrowed a friend's car. The plates aren't registered to you, but someone paid the tax and that's all they care about. The second way is to see if either state (yours or the one where the car is) will issue a temp tag for the vehicle. The third way is to just drive it without tags, which is a totally different ball of wax. In some states, the bill of sale and signed title serve as a 30-day temporary registration. You might get pulled over, but produce the documents and you should be good. The problem comes when you're crossing multiple states. Such was my problem when I bought a van in NC and wanted to bring it to PA. PA doesn't do temp tags. NC does, but it was during the pandemic and getting an appointment with a DMV notary was going to take months. NC is pretty lenient about letting you drive without plates as long as you have the papers, but what about VA, WV, and MD? Instead of diving deep on that bit of research, I just took a trailer and towed the van back.
The secret is to research. I see you're in MA, right? Does MA have DMV notaries? Or do you go straight to the DMV? Or can any notary do it? Find your resource and ask.
Another relatively reliable source is www.DMV.org. It's a non-profit site that is kind of the Cliff's Notes of every state DMV. It is not always correct, as it's hard to keep up with every law change in 50 states in real time, but it's a good start.
Check with your insurance agent, but for the most part your insurance laws in your state cover you where you go. In PA, if I buy a car I have 30 days to inform my insurance company. It is de facto covered (liability only) as long as a liability policy is in good standing on another one of my vehicles. If you want collision or comp coverage for the return trip, make sure you talk to your agent about how the underwriters will or will not cover the elective part of the policy. You also need to see how insurance plays with the other state when it comes to temp tags. When I was asking about getting temp tags for the van I bought in NC, they don't just require an insurance card, they require an insurance card from a company that is licensed to underwrite in NC. Fortunately I had State Farm which does, but if I had Mercury, I wouldn't have been able to get a temp tag.