@Rasa39 here is pretty much right, but for some clarification;
3.65 is a little bit of a hard upgrade, admittedly, and the main downside will be that recovery from a user failure in the system partition will basically boot you back to vanilla unpatched firmware, thus making you wait until the native 3.65 Enso hack.
However, most (if not all) plugins are going to be made with 3.65 in mind alongside 3.60, and (most importantly) you'll be able to play unpatched/NoNpDRM games that you couldn't on 3.60 -- and that's a
lot of games. And you'll be able to get updates for said games as they come out as if it were installed from the PS Store. Plus, most fan patches will be made with NoNpDRM-patched games in mind from here on out, so consider MaiDumpTools and Vitamin deprecated.
You CAN get some of said 3.65 games dumped via said deprecated tools and running on 3.60, but who knows the validity or functionality of those dumps with these one/two-year-old programs? And said fan patches or regular OTA updates won't work either without being made for/patched with MDT/VTMin, which is going to be a hassle more than anything else.
Anyways, online should work should you spoof your firmware version properly; it should be set to 3.67 or 3.68. If not, a 3.65 Enso upgrade wouldn't hurt (aside from updating your plugins beforehand).