There's no need to move slowly. I'm a 23 year old grad student. I got my first credit card 09/2013, and I've now got 10 credit cards. Despite this, I still have a Transunion FICO score of 730. The signup bonuses I got:
10k Amex Membership rewards points
50k Amex Membership rewards points
50k US Airways Miles (converted to AAdvantage miles today)
$444.44 from Barclaycard Arrival+
$25 Sallie Mae Mastercard (got this for the 5% on groceries, gas, and bookstores - includes Amazon, not the signup bonus)
$50 Fidelity Amex
You can read all you want about credit scores but you need to keep the bigger picture in mind. So long as you don't want a mortgage, car loan, etc. in the near future, you really don't need to worry about your credit score. You say you won't need anything for the next 2-3 years so you'll be fine. Just apply for whatever you want. If you are harming your credit too much, then you'll start getting denied credit cards, and you know to slow down.
Despite my 10 cc's gathered in less than 2 years (and I actually had only two cards until 08/2014) I still have a 730 TransUnion credit score (as reported by Barclaycard). This is my true FICO score. Sites like Credit Karma, Quizzle, and Credit Sesame are credit score estimators. Being estimators, they can be incorrect. For example, right now Credit Karma estimates my Transunion credit score at just 694.
Don't take the estimators' scores at face value.