Weller, JBC, Ersa and Hakko are generally good brands to choose your soldering station from. There are some Chinese Hakko clones out there for a budget price, which will do a pretty descent job too:
… especially when equipped with an original Hakko soldering tip (which indeed fits on those clones).
You don’t necessarily need the schematics to build your own OSSC. Essentially you just need the bill of materials (BOM):
There you can find the designators for every part, which are printed on the PCB itself too. That way you can see where every part belongs to. You just have to keep in mind, that the ICs have to be soldered with their marking showing in the right direction and that some parts (like diodes) have to be soldered with respect to the right polarity.