In general it depends what you want in a race.
The TEC are all about their economy. Their overarching strategy is that they try to force their enemies into a war of attrition where both sides suffer casualties- but due to their strong economy, they can replace losses far easier then the other factions. One of their most notable units is the Ogrov Torpedo Cruiser- Which is utterly devastating to enemy orbital structures, allowing even very small TEC attack fleets to be a mortal threat to enemy planets(consequently attacking on multiple fronts is a great way to force enemies into said wars of attrition).
The TEC in general have the most "straightforward" abilities & units. Simple effects with obvious archetypal roles are fairly common in their repetoire.
The Advent on the other hand are all about synergy. They have the weakest economy and their capitalships are fragile, but the Advent fleet is generally stronger then the sum of it's parts. This does mean that the Advetn by and large require more knowledge(you need to know all the synergies & combos to utilize them) and Micromanagement(they have a lot of effects which need to be employed optimally and very few of their ship's abilities can be safely left on autocast). That said, The late game Advent fleet is a thing to be feared- famous for being nigh-indestructible with proper Micro.
It's also worth noting that in general, the Advent are probably the most miltant faction. They by far have the worst economy, but they have extremely cost effective early game units(which give them a strong early game military presence), and late game when their fleet synergies come together their fleet is terrifying.
The Vasari are the game's premier late game faction. Their Phase Missile technology is hands down the best weapons tech in the game, and ruins one of the most important parts of the Advent fleet synergy(in general the Vasari vs Advent matchup has long been considered unbalanced as a result). Additionally their ships are in general more powerful, but less cost effective then the other races, which further contributes to their status as a late game race.
But they do have a few very potent tools for surviving the early game. They get access to starbases earlier then any other faction(which combined with their "assault Deployment" tech and the fact the Orkulus can move results in Vasari often using Starbases offensively early game by attempting to build a starbase in orbit of a key enemy planet). Also early game their scouts can capture neutral astroids which gives them an early economic boost.
That said, their economy, while overall stronger then the Advent tends to be a bit dependant on neutral asteroids as they get access to trade ports later then any other faction.
The other major vasari motif is "mobility". They get a ton of tools that give them a huge mobility advantage on the other races- Most notably phase stabilizers, which allows them to under certain circumstances plot phase jumps between systems not linked by phase lines.
Anyway, that's the general info. Of course subfactions add another decision to be made- But in all honesty choosing a race should be your first step.