Merry Christmas and Happy new Year to you too Mike,
I envy you for having the possibility to travel for 3 whole months in South East Asia, you must be excited by the trip !!
For the visa in Bangkok, you will get your visa within 2 open days if you choose for the normal, regular visa application process, which costs 800+ Baht. So if you apply Friday morning, you will indeed get your visa on Tuesday afternoon.
However, if you are worried to not get your visa in time, or if you just want to clear this asap, you can get the one day visa process for 1000+ Baht or the express visa process for 1200+ Baht. With the first option you would get your visa on Monday afternoon and with the express option you would get your visa on Friday afternoon, so that is up to you. If you do so, you would have 4 full days to travel around Bangkok without having to worry about your Myanmar visa.
Be careful with the hotels or guesthouses, you will travel during high season and then accommodation and hosteling being very scarce in Myanmar, it might not always be easy to find a room without booking. So if you can make a booking in advance, you should better do. Then if you don't know yet what will be your schedule, you better have several options for your accommodation, since guest house from plan A might be full, you should have at least plan B and C.
Hope your journey will be amazing, but I have no doubts it will be