Europa Universalis 3 - Page 44

I personally don't even bother sending gifts to anyone other than electors; answering HRE members' calls gives about +100 relations with *everyone* in the HRE (and denying those calls is about the same but negative), so answer a few wars and make sure never to miss any and you'll have +200 with everyone. If you aren't getting any calls, don't worry; they'll happen eventually (a lot of new players seem to expect massive changes to the world in 10-20 year periods, which rarely actually happens). From there, just bribe people who you have to go to war with once the war is over. Also make sure you get a winning peace deal (even if it's just them conceding defeat) for the extra +10 authority.

Other than relations, keep your Diplomatic Skill up (hire an Ambassador, add lots of nations to your Sphere of Influence whenever you have spare prestige), and make sure people don't convert en masse (people of different religions are very uncooperative no matter what).

Another nice (and somewhat abusive) trick to farm imperial authority quickly is to annex vassals and then release them immediately after for the +10 bonus for a state being formed in the empire. The fastest way to do this is by releasing all possible vassals you have cores on (ex Milan, Styria, Tirol, Aquilea as Austria depending on who you killed thanks to missions/calls to arms), waiting for the 5 year truce to expire, cancelling their vassal status and then quickly wiping them all out with reconquest.

Beyond that, some nations just can't resist annexing the same people over and over, such as Brandenburg taking Pommerania and Denmark taking Holstein. Just make sure to leave those people strong enough to keep annexing those nations every few years and you'll have an infinite source of authority to farm (usually often enough that you can be at war with someone or other as often as your war exhaustion allows).

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If you want to aim to form the HRE and be a superpower from the start of the game, I'd suggest someone like Aragon, Castille, France, or Naples who will be grabbing up lots of non-HRE territory but not interfering much in eastern Europe (let Bohemia and Austria take all of that, it just means more land for you later). Vassalize 4 or 5 electors and keep them happy and you'll become emperor pretty soon, then add all your provinces to the empire for a big authority boost (and if you're close to unifying the empire release all your newly-empirefied potential vassals for a big extra authority boost; for example, as Aragon I released all the french minors, naples, the pope, etc for at least 100 extra authority). By the time you unify (probably late 1500s) you can take a good chunk of the world (in my case about half of africa, all of north america, and all of europe, as well as some random provinces elsewhere).

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That said, I'd suggest some roleplaying and aiming for smaller goals (and playing a smaller nation in general) for a more fun overall experience; early on the game isn't all that hard as someone like Castille or France, and once you unite the empire nothing in the game will even remotely challenge you. For example, playing Brandenburg and eventually forming Prussia and then Germany with historically accurate borders and few or no colonies can be substantially more challenging while still quite manageable for a new player, especially since later in the game you'll probably get absurd wars like France+Castille+England+Portugal+Austria+Bohemia at once if you don't bother to repair your relations, which can create a nice endgame "final boss" situation.