Ottomans has always been the easiest nation for me to play. Day 1- declare war on every Anatolian minor you have a core on. Doesn't matter you don't have the army to take them and the Timurids out, yet. Start minting a lot- you'll take care of that inflation later. Build army. Take out the minor nations ASAP. Ignore invading Timurid army until the minor wars are done. Take back any Timurid-conquered core territories, but no more (peace out with concede defeat (either way) once that's done).
Hopefully, by this time, Timur has died in battle, so then the Mamlukes will take out Timurid territories adjacent to you- Viola- no more Timurid worries. (despite what your missions would have you believe, the Mamlukes are your friends until the Timurids are good and dead--you can always take the Mamlukes out later as you tech faster then they do).
Cycle through missions (while everything else is going on) until you get 'city of the world's desire'. Take down any adjacent orthodox nations (Byzantium, Georgia, Trezibond, Albania, etc--unless they have a really good ally).
By this time you've either put yourself on the border of the Golden Horde, or they've come to you. If you're not ready the first time, I don't blame you, just peace out ASAP- even if it means giving up money. If you border Qara Koyonlu, Colonize their non-wool provinces (like Georgia's gold), but just occupy the rest for as long as possible- if a revolt starts to get out of hand over there, demand tribute- demanding tribute from Qara frequently leaves them without the ability to raise an army.
Second war with the Golden Horde will also be your last. Conquer and colonize as many territories as you can (that will not make you border another horde) occupy as many as you can beyond that. Did I mention the armies and the colonies require some major minting? Keep at it.
Build a center of trade as soon as you can- most of your acquisitions will trade through it, and you need the $ boost (for historical reasons I always build it in Thrace...).
If at any point in this process you get the mission 'conquer southern Greece', and the Catholic defender of the faith has a weak navy (eg. Burgundy, Bohemia) take them out. If you get in defensive Holy Wars against Poland or Hungary, all is going according to plan- take as many territories as you can from them that will not get you a common border with either Bohemia or Austria.
Colonize the rest of the GH and be prepared to occupy/colonize the other hordes. (I like keeping opm hordes around for the colonist boost)
Colonize Siberia (one of the richest places to colonize).
Build a fleet to match anything GB can throw at you, and now you're ready to stomp Europe.
By now you can stop minting, and probably will not have to mint for the rest of the game.
(By the 1650 disappearance of 'Holy War', I've owned/Vassalized everything but GB, Iberia, and Switzerland in Europe without ever crossing the infamy limit using this strategy <normal difficulty>. PS I never raise war taxes in any game I play, so I don't know how that may change outcomes)