This is such an individual decision! I was a SAHM for 7 years and now I'm a full time student. Both have their pros and cons. Here's my list anyways
Pros of SAHM -you get all of the firsts -your house will be clean -you can make nutritious time consuming food -you have time for hobbies -there are lots of ways to socialize your kids as a SAHM- go to playgroups, library storytimes, playgrounds and meet other moms -it's low pressure: jammie day can happen. You can go to the park and just chill with the kids. hide and seek is always on. And if you screw up and forget to take the chicken out of the freezer nothing bad happens. There aren't any deadlines
cons -it can be very lonely. You NEED to find some SAHP friends or a regular playgroup or you will go bananas. -the work you do is often overlooked and it always gets undone. -Every day you wash the same laundry, and the same dishes and put the same toys away and read the same stories and no one says thank you and it gets old -without a lot of external praise or daily variation it can be dull
Pros/Cons of doing the student thing (might be similar to working?) Pros -I get social time -finally I feel like more than just a mom and it's a nice feeling -I feel like I'm accomplishing a lot and I love the stuff I'm learning -it's nice knowing that in 3.5 years I will have some money (if you're already working the having some money part is a bonus for sure)
Cons -childcare gets complicated. Who stays home when the kid is sick (and too contagious for the nanny). I have 4 kids in various stages so it's a headache and a half -you do miss them, a whole lot. you miss stuff. that part can suck -kids get sick at daycare all the freaking time (with a nanny, they wouldn't though -my life. is. insane. I don't ever have enough time for anything. there are not enough hours in the day. My formerly immaculate house is a disaster. Laundry is a Situation. Kids eat way more chicken nuggets. It's hard to keep up with school too. Definitely more stress -I don't have time to do all that fun pinteresty stuff. I used to be crafty and do fun stuff for my kids' school. Now I'm That Mom who never remembers to send a plastic spoon with her kids' thermos lunches of pre-microwaved alphaghetti.
For me, I'm glad I was a SAHM for a while. I loved being a SAHM for many years. and when I stopped loving it I went back to school and I am loving that now. I have no regrets about either situation. But only you can decide what is right for you. IMO both options are great options, you just have to ask yourself which you prefer.