Should I apply for a multiple entry visa or can I just use a single entry visa for my 5-6 month stay in Thailand?

You can apply for a single entry visa. You can download the form from the thai embassy website must complete in blue ink.

Put phone number under picture on back page. I think the form is titled re entry permit

You can apply for a multiple entry tourist visa (if your consulate will sell them - not all do). It would be valid for 6 months from the date of approval and on each entry you’d get 60 days (of which you could extend for a further 30).

You haven’t stated your nationality, but if from an approved country you can enter visa exempt, which would give you 30 days on entry - again extendable once for 30 days.

There is no limit on how many times you can enter (by air) on a visa exempt - apart from at some point an immigration officer may question why you are trying to do so. Whether that would happen is purely up to the immigration officer you hand your passport to on arrival.