Perhaps thegeoman could give you a better advice....
I've got some tips that have served me very well throughout the game (i've been F2P for nearly a year and a half). Just as a baseline: SRs are pretty mediocre in every way, even the best SR's high stat is lower than the worst SSRs low stat. It'll take a while to get yourself any SSRs, so take it slow and don't waste resources chasing ghosts.
Sadly there is no way to 'fast level' outside of spending your green energy restore things. IMO those are better saved for events but you can use them to level quicker if you like.
#1 GOLDEN RULE: Never roll your gatcha tickets unless there is a 3x rate up for SSRs(usually once a month)
#2 GOLDEN RULE: Never use your consumables unless you are grinding out an event
Other advice i can give:
-Payoffs in the form of fully corrupted girls are few and far between, before you commit to a character make sure you like their fallen form. To me, having a good corrupted artwork is more important than a cards stats because that's what we're in this for at the end of the day. Many cards are just color swaps or clothing re-draws, but the best ones to me get a completely new drawing for the last form. The best way to check is to right click the card image and select view image, then adjust the final number in the URL. 0 is 1st form, through 3 for final form. Using my favorite card as an example:
http://img.games-ent.com/img/card/base640/card_293_0.png
http://img.games-ent.com/img/card/base640/card_293_3.png
(You can also adjust the 3 numbers before that last underscore to view the other cards in the game. The SSRs are 250-350 and 400-450, they are the only ones with fully corrupted forms. Often you can find unreleased artwork using this method as well. Feel free to not actually play the game and just use this method to check for new card art periodically lol)
The best place to get SSRs are the quest event and the raid event.
-Quest events have basically 2 levels, the first part can be cleared using only your natural stamina regen. This level ends with the SSR for the event as the boss (usually). Make sure you use the guaranteed capture item on the boss (they usually give one out just before you fight them, its the purple band thing with the skull and the left button on the capture screen). The 2nd part is the 'extra' levels where costs start getting stupid. The final route boss of this part has both a 2nd copy of the event SSR and a wildcard. As an estimate, it takes about 5000 stamina beyond your natural regen to clear this part. It's not really attainable until you have a 100+ stamina bank from levels IMO, so hold off on this until your account levels up a bunch.
-Raid events are the ones where you run into event bosses while playing the normal story campaign. Raid events are nice for 2 reasons, 1: you can use your friends list to have a strong fighter with your team, and 2: if you fight the SSR for the event, theres a (small) chance she'll drop her card as a reward. This is also the only point in the game where friends are relevant. There are a few SSRs that block boss attacks, but the best one is the brown haired maid in a bikini top with a broom because she can block any boss attack. People don't usually put her as their leader unless there's a raid event (because she looks meh), but its best to stock up on friends who have her. Don't let the big numbers scare you, its actually much easier than it looks to get rewards for this event than the high numbers on the 'rewards' tab indicate even with an only SR team, and that's because near the end of the event the crazy whales will start finding high leveled bosses they don't want to fight and 'sharing' them with others, clear these out for tons of points.
As far as figuring out what your stuff does, I use this website
http://heroine.webcrow.jp/album/index.php since you cant translate the game's text directly. It's updated on a pretty regular basis, but it takes a couple weeks from when a new card is released and when they have the info.