I went in April for 10 days or so. I left a bit underwhelmed, but looking back it was a fantastic experience and am glad I went.
I can recommend not going in April, it starts to get v hot and everywhere is dusty. Nov to Feb are the beat times to go. Only had enough time to do the "big 4" (yangon, inle, mandalay and bagan)
Travelling is pretty easy, the infrastructure is very poor however (for obvious reasons)
You must avoid the trains (government owned) so that leaves buses and planes.
The people are fantastic, probably the real highlight for me, so friendly, happy to see you, even if they don't tell you (despite opening up some people will not talk of the oppression etc, old habits doe hard etc)
I was surprised how expensive it is, so be prepared for that, far more expensive than Vietnam and Cambodia etc.
I'd book your accommodation early if going in peak times, tourism is growing rapidly but there is a lag of investment for hotels guest houses etc.
If you have any direct questions please feel free to email me direct.
If you're there for a month you should be able to see a fair chunk of the country (the bits that are open....anyway )
Edit: you've probably already decided that its moraly acceptable for you to.go, but be prepared for it to hit home when you're there. You will travel on roads built by forced labour, and see sights that have been renovated by forced labour (mandapay palace, don't go in) and there were times when I was there that I wasnt comfortable with this.