Need help regarding car sale out of state

I am looking at a vehicle in south MS listed for private sale but am unsure of how the details of the process would work. I'm looking for any guidance as I, being the cheap person I am, have had the same car since high school and have no experience purchasing a vehicle.

I live in LA, car owner is in south MS. Carfax is clean, the vehicle looks good and asking price reasonable. Questions I have, should I decide to buy after look, test drive, and mechanic inspection are as follows:

I intend to pay cash (i.e. cashier's check) but my bank is not located in MS. Can/should I pay with a personal check since there are my bank doesn't have a branch near seller and have him deposit immediately?

If the private transaction is made, do we need to transfer titles that day so that both parties are present? If so, how does this work if the vehicle will need to be registered in Louisiana? Would I have to pay sales tax in MS or LA?

Please excuse my ignorance on the topic. I appreciate any insight. I am looking into this private sale as it seems the best deal I have seen but I don't want to get screwed on sales tax, multiple trips, DMV visits, etc that would make it a bigger headache than its worth in monetary savings.