Don't get any agents involved, they aren't going to provide any value in such a deal.
A lot of lawyers will handle house sales for a reasonable flat fee. This is how we bought our current house and will buy our next. I would get your own lawyer and tell the seller they should get their own if they want. You can even have your lawyer recommend another for the seller to help walk them through the process, it will probably make things smoother overall.
In our case it was a $750 flat fee and they would write up to 10 offers and represent us through closing. Closing lawyer costs are several hundred anyways, so it was a reasonably good deal. The lawyer wants the title insurance commission, which is pretty lucrative. We live in competitive north east market and ended up doing 4 offers on different places. Not having an agent makes the sellers agent salivate as they often get twice the money. We actually were not the high bidder, but the selling agent kicked in the difference plus a little extra to the sellers to make them whole and get the bigger commission.
You can go it alone with standard online contracts, but because you will need a lawyer as part of the closing, you should just engage one now as it will be very cheap. Just make sure they can close for any of the places you might get a mortgage from.
1) Get a lawyer and maybe one for the seller
2) Have an offer put together, include inspection and financing contingencies unless the seller has a problem with these. You will provide this with a small deposit of something like $1000 to be held by the sellers lawyer in escrow.
3) Have the offer agreed to. Seller has agreed to sell and doesn't really have a way to back out at this point as long as you meet all your requirements.
4) A purchase agreement is then put together, which is basically the long detailed version of the offer letter. Everyone agrees to that. After some of the contingencies are cleared there is usually a larger payment made around 5%, put into escrow.
5) In parallel you work with the bank to line up the mortgage (shop around).
6) Do your inspection, you can do it yourself if you know what you are doing or don't care. The bank generally doesn't require an inspection, just an appraisal.
7) Get approved for a mortgage and do the closing with your lawyers. Should be able to do it in 30-45 days depending on your bank.
Get a lawyer though, they should be able to walk you though this quickly and are actually pretty cheap for this sort of thing.