My first game was as Austria (not counting the demo), so yep! I have a lot for 'ya.
So this is gamey as hell, but on D1 a LOT of countries have disputed successions. From what I can tell, Hungary is always one of them. D1, Royal Marry Hungary. As soon as you can, claim their throne. Then, as soon as you can, declare war on them for their throne. You may want to ally either Bohemia, Poland, or both to assist you in this war. If Hungary picked powerful allies this war may not be winnable - if that is the case, restart and try again (given you're only about a year in at this point so restarting is no big deal). They're a very powerful ally, so I'd keep them around for awhile and then annex them whenever it's convenient for you. Naturally you want to improve relations with them as soon as the PU forms so that the PU doesn't break (it will break if their relations are below 0 with you when your monarch dies).
You'll want to keep a close eye on disputed successions. In my game I PUed Hungary, Bohemia, and Poland by RM+Claim Throne+Declare War (maybe Bavaria, too, I forget). I managed to PU Russia, too, but I think it was a little buggy because they converted to a Noble Republic and things got wonky, so the PU broke. Anyway, you'll also want to keep the electors happy. Bohemia will always vote for you if they're in a PU with you. A lot of times I'd have another vassal as an elector. This will make the other electors mad, but seldom are the other electors coordinated enough to have the remaining of them vote for a single person. So typically if even two electors vote for you, you're good. That said, you can typically stay as the emperor forever. Don't ever use the "Enforce Religious Unity" option unless you've passed the reform that disallows internal HRE warfare. It gives -25 relations with ALL HRE members, and ticks away at only 1.5 a year. Plus it stacks. Before I realized this I had -75 relations with all HRE members... which made passing reforms difficult. If you must use this option, use it sparingly (wait for the relations to come back up between usages). Eventually you will be able to form the HRE, but this didn't happen to me until about 1700. It takes awhile to build that imperial authority.
For NIs I'd go with the Diplomacy tree as one of your first. Faster fabricating+cheaper cores+more diplomatics+better relations is outstanding for Austria. It's a great idea anyway, but especially for Austria. I'd also go with the military ideas. In order I'd do defensive, offensive, and quality. I wouldn't focus so much on colonists. Unless you beeline towards colonization, you're going to be beat by Portugal, Spain/Castille, Great Britain/England, and France. You have too many juicy targets all around you to be focusing on that.
Your biggest enemies are likely to end up being France, the Ottoman Empire, and later Sweden and Russia. When you annex Hungary the Ottoman Empire will hate you forever since they'll border you hard, so be prepared for that. France will constantly declare war on your OPMs within the HRE, who will request your aid. It sucks to have to say no since you lose imperial authority and relations, but don't be afraid to say no. Check France's military power against yours (+factor in your PU members partially) before accepting that call to arms - if they're way above you, fighting the good fight won't do you any good and you'll get stomped. Declare war on France when they've been weakened - usually either by fighting GB or Spain. Unfortunately, this will occasionally never happen... it's sort of a luck thing.
Something to keep in mind: the Netherlands will revolt all game. It doesn't matter what your revolt risk is... it's an event that happens over and over and over and over again the entire game, and the longer the game goes the bigger the stacks get (mine are typically around 30 strong at 1755). You'll have a big stack around there because of France anyway, so it's no big deal but it gets annoying.
I now control most of Europa aside from the west coast + Iberia and most of India (I was trying to get the achievement for taking over India as a European nation). Unfortunately for every province you control, coring is like +5% longer. I'm up to the point where coring takes about 10 years per province... and if I go anywhere over 100% overextension I get about 3 revolts a month - often times with stacks upwards of 50 rebels. At any given point there are typically enough rebels in my land to, if they were a nation of their own, have the second strongest military in the game. It's not very fun anymore, but before you get to that point it's pretty fun playing as Austria.
:Edit: Oh, I forgot. You'll get a decision to become an archduchy. It's basically the same as the default monarchy (despotic monarchy? I forget) but it's +1 relationships, too. This is nice but you're never able to change away from this government type (except via events that would change your government type). So look at the different types of monarchy and determine if you want that before accepting to become an archduchy.