Thing in the picture is solder pump, mostly useless unless you want to desolder some old through hole shit without damaging it or using 10 cm of wick.
There is no "best tip" they are all situational, but usually some C type for general, sharp and pointy for 0402 smd and K type for big connectors and etc.
As for soldering iron its all about the tip, don't cheap out on it. More power or precise temp regulation is situational most of the time.
Chink t12 soldering irons are 100% worth it and I would prefer one over oldschool 200$ "western" soldering station