How much does my civilian career affect what I branch as a National Guard officer?

You need to see what slots are open in your state. Call the units and talk to them. They'll know more about what will be open down the road also. I talked to a couple of different units before making my decision. Both had slots and both were willing to add me. But one was closer to home and was the quickest path to company command. If you can meet with them and they want you, they can pull some strings to get you.

A quick look at the units in the NYANG says you probably won't have any issues getting Infantry. You have 42nd. Div Headquarters and a full Brigade Combat Team, plus and Aviation Battalion, so there should be slots AND opportunity to promote, at least through the company grade Officers. OTOH, there seems to be only one Battalion of Engineers, so slots and promotions may be harder since the numbers are very large. Looks to be a Heavy unit, so real construction instead of Sapper Work.
I enlisted Infantry and Commissioned Infantry, then Branch Transferred to the Combat Engineers when I moved to Kentucky. I'll always be a Grunt at heart, but I had a couple of position as a Combat Engineer that were the best jobs I had in the Army, Active or National Guard (Sapper Company Commander and Assistant Brigade Engineer). At the time I made that switch, Kentucky had two full Battalions of Engineers, a Corp level (Heavy Engineers) and a Divisional Combat Engineer unit that supported the 35th Division and also 3rd ID Europe when they were short handed on big exercises. Had I went back to Ohio with it's large National Guard Infantry unit, 73rd Brigade (Air Assault) Sep. when I was living there, I would have probably stated a Grunt. If you are looking at it as a career, find a branch that is large enough on the State level to promote and that you want to do for awhile.

Good morning! I just graduated OCS a few days ago so I'll try to offer as much fresh insight as I can. As a NG officer you will receive your branch from your state, based upon their respective units' vacancies. The only folks that create their top 20 choices for branching are active duty candidates. If your state doesn't have infantry units, you would have to join into the NG of a state that does. Same goes with engineer. Ask your recruiter what those vacancies look like.