Okay.....
welcome to the club

first thing to remember is its not that big a deal for you to buy girl things
I know that sounds silly and right now you are freakin cuz you feel its impossible
Ok, first thing is maybe drive farther away from your home, maybe a hour... where you wont feel so exposed
When I first started, I would buy a few things and buy a gift bag and birthday or anniversary card at the same time
made me feel like they thought it was a gift
you will find that its hard to size yourself for a little while. Check out online sizing guides for your measurements
Thrift stores are your friend, many have specials weekly or daily where certain things are a dollar or half price. This lets you scoop up several things for little cost and try them out. You will make many sizing errors and its best to pay second hand prices rather than full cost and maybe shipping fees. Also visit garage sales, another place to get things on the cheap.
I always played the "its for my girlfriend" routine, shes about my size....etc. Garage sale women LOVE when guys shop for their girlfriends or wives.... they thinks its so adorable

I used to carry a shopping list, a fairly large piece of paper so I could hold it up a bit and look it over while I was in the girls stuff.... for me it just seemed like I was buying from a list that I was given by my wife, you may wanna write stuff on it though just in case

As for makeup, get on the phone and call a few department stores and ask for the makeup counter, when you hear a super great friendly voice, just ask... "Are you ok matching transgender customers? Or Im transgender, would you mind if I came in for makeup advice? My first call was ok and I went right in, many are bored and waiting for a customer to work on so they dont have to do busy work or clean. Let them match your foundation, powder, etc and go as far as youd like, if they do a complete workup you dont have to buy everything. Just be honest and shake off the nerves, its not as hard as it seems. Once you get your foundation and powder match, you have a key. Those numbers can be used on a website called Findation, you can then find the other brands that are a match to that. I have a giant list in my purse! Then you can buy from drug stores or walmart where foundation is 10 bucks rather than 50!
You will feel skittish at first, thats normal, but it gets easier everytime you do it... I promise
Just go in like you own it and be confident even if you dont feel it....
There are more people in the world who dont care or wont notice or bat an eye than there are that do care.... even though it seems we are being the center of attention, thats in our heads. Just do it!
Good luck and have fun I dont even break a sweat buying anything these days.... and I was the most scared person ever when I started!