I am wondering if there's anything a newbie should know about these. I mean, in Aigis, for example, every 50 Sacred Crystals you use upgrade your Stamp card for the next month. Also there are events running that buff your chances for rolls, etc. So I was wondering if there is any point in saving up the tickets. There are definitely events running in DP, but I am not sure what do these events do. And most confusion - what tickets have events running for them and what don't...
There are a multitude of different ticket types in DP but ultimately, there's no reason to not use them as you get them. "Gacha Events" don't affect ticket rolls. For example, the current Fever gacha is its own separate gacha section (and no tickets exist for it, you need to spend Nutaku gold for it).
Rare Gacha tickets generally fall into Rare, SR % chance and SSR % chance, and sometimes you might get Friend gacha tickets. First 3 are self-explanatory, the last is vague at best and seems to be more or less a Rare ticket obtained in a different manner.
Raid Gacha tickets are acquired from killing Raid or Area bosses. The most common boss is Sin, so you'll inevitably accumulate more of her tickets than any other (besides the generic Raid tickets). Raid tickets generally give N or R rarity, with the occasional SR thrown in. A boss-themed ticket is the ONLY way to get the R and SR versions of that boss (so if you want to Limit Break MAX a certain Quest boss, you'll need to run the 9 areas of that boss numerous times since you generally get 1 Boss ticket from the 3 area fights if that, since the only other way to get boss tickets for Quest bosses is the Rare Quest Boss spawn which is, well... rare...) Generic Raid Gacha tickets give N or R cards, drawn from the same pool as all the Boss-Specific tickets except they exclude the Boss cards (as mentioned, the bosses are exclusive to their own tickets)
Normal Gacha is rolled with Gacha points, and has a very high N rate, the occasional R and VERY rarely an SR. But it's the easiest to accumulate, so this is to be expected.
As far as saving your tickets If you've gotten all of the SSR that are in rare gacha (you can check by going to gacha scrolling to the bottom then clicking on obtainable cards) then you should start saving basically all of your rare tickets and Sr/ssr% ones. Currently there is the p2w gacha (has at least 6x more ssr then free gacha) and the free gacha. Free gacha has never been expanded but it should be eventually, Japanese version has toooooons more cards in their free gachas.
Its also rare to get any p2w cards if your f2p. We get a free fever ticket maybe like once a month but don't expect much from it. Currently you can actually get multiple from the dpp campaign.
So basically save all your tickets once you have the free SSRs cause nothing changes for free tickets ever . If you ever need fodder to lvl up your cards stick to the various raid tickets (horoscopes the best for it).