First US visa stamping is an important event. Do not mess this up or you'll keep getting questioned or rejected for future visa requests. So if you're not sure if she can get a F-1 comfortably, err on the safe side and apply for a H-4. Once in US, try changing to F-1 (see below).
F-1 versus H-4:
I would recommend F-1 instead of H-4 if you are not going to apply for I-140 or I-485 while she is on a F-1 visa. This is because F-1 gives her much more flexibility as she can get a SSN, can do co-op, then can get an 1-year OPT. With H-4, she almost has no identity of her own. Very painful status. If you are applying for either CP or AOS, bite the bullet and pay for her education and go for H-4 because F-1 to GC is a tricky change from what I read here. She being on F-1 also gives you the option to apply for a F-2 visa should you lose your job.
Applying for H-4:
Dress and act like a wife. Take plenty of evidence of marriage. Don't say a word about your intentions of studying or working in the US. Just say you're going to US to "look after your husband". Just do it. When you get here, you can study or try finding a H-1 sponsoror. Just don't talk about it at the consulate before getting a visa. Also, if you don't have a valid H1 stamp, I strongly recommend you BOTH go together for H1 and H4 stamping on a single appointment. Don't assume H-4 implies in-state utition. Some states like CA let you get in-state after 1-year in CA on H-4. Others like WA don't consider H-4 as residents at all. Make sure you document her residency by signing a lease, applying for Drivers License, opening joint bank account etc.
Applying for F-1:
If she has good chance of getting F-1, that is, good GRE scores and full funding (tuition waiver + monthly stipend + property/money in home country) go for it. If you don't have a solid F-1 case, I suggest you go for H-4. This is because H-4 is almost automatic. All you need to show is you're a valid H-1 and she's your wife. That's it - very simple visa. F-1 is considerably more complex. You can convert from H-4 to F-1 once in US but it'll take several months or so. And you'll need to document everything like ties to home country etc when you apply for the change and it's certainly not guarenteed to work. But the advantage is that you're already in US, so if they reject F-1, you have your H-4 to fall back on. All you will end up is paying for your tuition.
NOW read this VERY CAREFULLY:
F-1 is a nonimmigrant visa. She needs to prove that she'll return to home country as soon as she finishes studying. If you are going to apply for it, apply BEFORE getting engaged or married. Don't ever ever show anybody in the US as your sponsor. I suggest she comes to US as a F-1 first and after a few months, you get married here in the US, at least on paper. Then you can go back and get married in India. DO NOT marry a H-1 holder and try applying for a F-1 in home country. H-1 can be assumed to be immigrants, and so it goes that their spouses may immigrate as well. If you do apply for 140 or 485, forget about going to a F-1 visa from H-4. Also, if the H4 to F1 visa change is granted, you get F-1 status. You may still get a F-1 visa rejection if you try to get a F-1 visa stamp at a consulate, so if you do the H-4 to F-1 change, you're recommened not to travel till you have completed studies and changed to either H-4 or H-1 or AOS+AP.
