If you really want to save time, I suggest to learn only:
1) Presente indicativo (io vado, tu vai, egli va,....) (io mangio, tu mangi, egli mangia....)
2) Passato prossimo (io sono andato, tu sei andato, ...) (io ho mangiato, tu hai mangiato,....)
The first one can replace even the future and imperative.
The second one is the only really used past tense in the spoken language (very similar to your present-perfect but the difference is that you can adopt it always, whenever you need a past tense).
Even the conditional tense can be replaced by these ones...it will not sound perfect but everybody will understand you for sure! Bye