Depending on how you are going to travel, you should think about around $600 for a month, that is $20 dollars a day. At least that was more or less what I spent in 28 days, so that was for 1 person and I was in Myanmar about 1 month ago, so pretty up to date on that part.
In two weeks you can visit those sights, but it won't be fun, as you will be spending most of your time on busses and less at the sights. As Ben said, travel is slow, think 15 hour busses for not much distance. I would go for 3 weeks minimum if you want to do all those places and want to spend a little time at each, really 28 days would be the best amount of time.
You don't need to change money with the guys on the street anymore, Myanmar has opened up its banking system and the exchange rates at the banks or even at the airport are the same or sometimes even better then on the the streets, added bonus you don't have to be scared to be ripped off. Take more money with you than you think you will spend, you can always change them back when your return to Thailand. Better too much then too little!
Bills need to be clean, no tears, and preferably without creases, also post 2002, big heads, and none with the serial number CB if I remember correctly. CB's won't be accepted at all, non clean, with tears and a lot of creases might be accepted but at bad rates, same with older bills. Though it will be harder for you to find somebody willing to change those bills even at a bad rate. Rate a month ago was swinging between 760 and 800 per dollar.
So my suggestion, take 600 dollars for the 2 weeks, which is way too much, but as I said you can change back when you return. Of those 600 dollars, take 400 in big 100 dollar bills, and the rest in smaller denominations, 20's are not bad as they are neither too big, nor too small, a few 10's and 5's and maybe 10 dollars in 1 dollar notes. You want the 20's and other smaller notes for hotels which mostly ask for payment in dollars, and for entrance fees and such.
You don't need to change all your money in Yangon, though you get the best rates there. This however might have changed by now as it things were moving so fast now, that I heard for instance that at the airport at Inle Lake they were giving exchange rates of 800 as well, so who knows?
Also when you get change in dollars (for instance at hotels or buying an entrance ticket), be sure to be as critical as the locals about the dollar bills they give, scrutinize the bills, check for tears, creases, dirt, the serial numbers and the dates, because sometimes they try to offload bad bills on unsuspecting tourists. Don't be afraid to refuse a bill that isn't good, or you will not be able to offload it yourself later on.
To get you started, average hotel prices are 8 dollars a day including breakfast (so sometimes it is more, sometimes less), that might or might not include a private bathroom. If you want to be sure of always having a private bathroom, think more in the 10 to 15 dollar range. Meals are on average between 1000 and 1500 kyat (1.5 to 3 dollars), a beer on tap in a 'beer station' between 500 and 600 kyat, busses between 10 to 25 dollars for a 15 hour trip (you pay in kyat, so that is between 8000 and 22000) depending on the bus and the route. Entrance fee at Bagan is 10 dollars, I would suggest skipping the Mandalay ticket, but if you want it, it is 10 dollars as well. Entrance fee at Inle was I think also 10 dollars, but maybe it was less, I can't remember anymore. A taxi from the airport in Yangon to Sule Paya where the budget accommodation is centered should be 5 dollars if you bargain hard!