MTF I look completely male, but I would like to buy some women's clothing?

Men or male looking people in the women's section of a clothing store are nothing special. Probably people would think that you want to buy something for your girlfriend or anyone else, if they thought anything at all. You won't draw any attention on yourself.
If you want to try something on, you can grab some men's clothes, hide the women's clothes under them and go into the men's dressing room. Nobody will notice.
Besides, most people don't care what other people are doing and buying. So you really don't need to worry.

 

If you are buying women's clothes no one will notice. They might think oh that's nice he is buying something for his girlfriend. It's not like guys don't buy stuff for women. As for your second issue try taking your measurements using a cloth ruler. I googled how to take your measurements and was going to use that to start my clothing collection. If not grab some jeans cover up the ladies stuff and use the mens changing room. I am also new to this so my first time will be nice. Good luck to you hope it works out.

 

There are lots of stores that only have one dressing room for people of all genders! Usually I find them in smaller stores (ie, not department stores) like Gap/Old Navy/H&M or discount stores like Ross and Marshall's. Check out the scene when you enter the store and simply leave if it's too awkward or gendered.

You can also ask a female friend to go with you so it might look like you're just helping her out. This is especially nice if you have one you're close enough to change in front of since you can actually go in the fitting room together and any female clothes can still be assumed to be her selections.

Other than that, online stores! Look for ones that have good return polices. Lots of times they'll have free shipping if you spend enough. I always buy extra to meet the minimum, knowing that I'll return most of it.