I'm 20 years old, and currently working as an IT professional (meaning I am busy). I want to learn either Muay Thai or BJJ.
How many times a week is ideal for me to fully learn? Is 2 times a week enough?
If you go once a week, you'll make very slow progress. If you go twice a week, your progress will be mediocre. If you go three times or more a week, you'll make steady progress. Training five or more times a week is a whole separate level of learning. (If for some reason you're able to train many times a week, make sure you ease into it. Don't over do it in the first week and risk getting injured. It takes time to get the stamina to do five-plus sessions a week.)
Whether it's enough is up to you. Going twice a week can be frustrating because that ends up being the maximum--that is, if something comes up, then it may be only once a week, and your progress backslides.
As a beginner, you can make really rapid progress 2x/week (lots of material to learn, and you have no place to go but up). But as you get to an intermediate level, 2x will seem like treading water -- it'll keep you in shape and keep your skills sharp, but you won't improve rapidly -- but you'll need 3x or more if you want to keep advancing at a good clip.
Expanded version of my comment on Dave's answer
Those who can't get in the forth and fifth formal sessions a week can get some of the benefit by doing some solo work. Forms, bag work, footwork drill, and so on. There are whole books on the subject.1 You don't get the more learning, but you do forget less between sessions.
I also use these solo sessions as an opportunity to do some of the oddball things that people always recommend but are inconvenient in some class formats. Things like:
1 Links to a couple that I have and think are pretty good, but I have no relationship with the author and no interest in the books.
Some years ago I used to go wushu classes about two times a week, It took about a year for me to get to a 'decent' level, where I could do the basics, and a wee bit of advanced stuff. If you want to learn at a more accelerated pace I think you should consider slowly increasing the number of workouts per week.
In my opinion you should start out slow and then increase the frequency of workouts. (I work in the same field as you and I understand the sort of workload). I practice 6 days a week. Here is how I did it:
I started out with wushu, early mornings 4 times a week on Tue, Thu, Sat, Sun. It took about a month to get used to this routine. (Mornings are the best because you are not really missing out on your social or work life.) A month and a half later I started going to Kalaripayattu classes on Mon, Wed, Fri. The result of this is that in two months I've gained the same level of fitness that took me a year earlier.
The key here is variation, I don't do the same exercises everyday. I mix up taolu, sanda, body conditioning, gymnastics, weapon practice and so on.
Later on I plan to introduce soft styles to balance out the hard exercises.
Couple of random pointers: