1) How early should I begin building a fleet, or should I be focusing on taking planets and using my resources to build structures and defenses? And what should my fleet consist of, are the early friggets nice to build up a lot of, or should I focus more on the stronger ships?
You build a fleet so that you can take more planets faster. Early game expansion is critical because it determines your future economic potential. Developing them with defenses and trade ports should come later, after you've taken all the neutral planets possible, since these repay themselves very quickly and give you more logistical slots to develop later.
As for fleet builds it really depends on your style and your race. I like corvettes because they can take out LRFs and siege frigates quickly, but they don't do well against much else, and as Vasari you should probably avoid them entirely as they are a tier 2 tech. Just go strait for assailants, and I wouldn't build much else early on besides sentinels if your opponent tries to counter them with corvettes.
2) When should I begin taking upgrades (armor, health, damage etc.), is it something I want to get from the go and keep going constantly, or are they sort of, get them for the late game?
A couple of the first tier upgrades are alright if you have a bit of extra cash and don't want to increase your fleet supply yet (and thus permanently hurt your economy). Anything higher level and isn't a prerequisite for something else good should wait, 5% bonus to anything isn't much early on, but once you have several hundred fleet supply of ships it makes much more of a difference.
One big exception to this is phase missiles. I wouldn't build military labs just for them, but as you build them for new ship types max these out ASAP. Once upgraded they are by far the most deadly weapons in the game, and your most important damage dealers like assailants and bombers use them.
I am currently playing Vasari, are there any key things I should be building/upgrading 100% of my games.
The phase missiles as mentioned. Phase stabalizers are also a god send later in the game, but if you're Vasari loyalists your titan can deploy them so you don't even need to research them in this case. Your starting cap should probably either be a Jarrasul evacuator for faster expansion and cap killing power later, or a Skirantra carrier with for raw combat power and dealing with the militia faster. Once you start running into titans the Kortul battleship is amazing, and it was my favorite capitalship back in Diplomacy. Overseers are your repair cruiser, and no matter what race you play as you should get some ships of this type. And if you really want to get into their more elaborate tactics, subverters and mine layers can do some mean things.
That said, much of what you should focus on as Vasari depends on your subfaction. Loyalists for example will mostly be building civic labs trying to get stripped to the core, while rebels will mostly build military labs at first trying to get to Starbase Mobilization.