You can go with pretty much any syndicate you want but the most practical combinations are:

Arbiters of Hexis + Cephalon Suda + Steel Meridian

New Loka + Red Veil + Perrin Sequence

The way it works with these syndicates is that when you farm standing to one, you lose standings on their opposing teams. These syndicates combinations does not conflict with each other at all, so you can freely farm for standings on those three without having to worry about losing any.

Each syndicate has their own benefits, so it mostly depends on your own personal needs, which weapons you'd like the most, which augments you need etc. Keep in mind that most of their items can be traded, so even if you're an enemy to, let's say Red Veil, you can still get their weapons through trading with fellow players