Take the mission against Byzantium, finish Albania as fast as possible and then DOW Byzantium, send 7 regiments to each one of the 4 provinces. Take all the byzantine stuff, Athens will become a vassal.
Change capital to Constantinople via decision, then change back to Edirne burning 200 admin points. Do take the Devshirme System when you can.
Attack Venice (and Cyprus if necessary) to take enough greek provinces to culture shift to greek, concede to Orthodox rebels to become Orthodox. RM Athens and try to integrate them rapidly if there aren't enough greeks to go around. Then tag change to Byzantium via decision, you might wanna wait until you have the mission to conquer the Levant from the Mamluks though(good time to take your cores back as now they'll expire much faster). Then dow the Mamluks (you may consider resting for manpower if you need to every once in a while, don't sweat it). You want to take Sinai and Negev in this war. This turns all the mamluk land in Asia into colonies, meaning you can pick up any Asian territories they have for ridiculously low warscore(and they'll be weaker). Since the Europe/Asia border is between what is modern Turkey and what is modern Syria/Iraq, I personally would suggest letting those be colonies to you as well until you cored them (therefore not taking your Turkish cores), because that will give you I think 212% OE iirc of the top of my head so if you have reconquered Anatolia, just release Syria and Iraq. Reconquering Anatolia also means you can restore the theme system, putting you back to Constantinople which now has over 20 base tax. You have the Ottoman ideas which give you triple manpower in religious wars (and there are like 4 orthodox states, mind you) and both the theme system and the devshirme system, which essentially means you probably have more manpower than there were people living in the world at this point in history.
From here it gets confusing for me because I don't play 1.4 and so can't say exactly what is the best course of action. Despite coring cost and time being a huge deal now, I would suggest expansion first to vassalize Qara Qoyunlu and the Timurids as soon as you can and then going up to block Russia off from Siberian expansion. I think the Ottoman tech group can vassalize hordes instead of establishing protectorates, so this is a viable strategy that is better off done before Persia rebels as Persia is in the muslim tech group and thus you don't get overseas expansion CB (also, admin on first idea group is never a good idea). You might wanna keep on friendly terms with the Timurids just so you can stop those rebels yourself if it becomes a necessity, because Persia blocking the way is easy to kill but a time waster. On the southern front is Africa, useful to expand to for trade and because your direct land border means those provinces are not going to be colonies. Might as well have some place to use those colonists. You basically have a monopoly on Asia and Africa.
The HRE is quite useful for the bonuses it provides (even less cost for coring and free vassals), and you might end up needing to reduce the number of Turkish provinces you have to culture shift anyway(highly doubtable), so you can release Aydın and the other Turkish minor and sell as much of Anatolia as you can at some random interval, then dow Urbino and get in. Do note that moving capital back to Constantinople won't cost anything as either the Theme System decision or the Form Byzantium decision automatically should do it. However, I would say that 1. This is pointlessly weakening oneself for a while and 2. You are Rome AND the Ottomans. You don't do diplomacy, you conquer. So just keep expanding into Europe until you can vassalize the electors. It's a good idea to get a truce with the Emperor so that you can dow electors freely, and you might just suck up the stab hit if necessary.
Otherwise in Europe, I tend to go for Venice as a trade node because I don't colonize the new world as the Ottomans (old world is best world) and it's an end node, but now that Sevilla is an end node and the Western trade node means "you don't need to colonize, you just put your navy in the Atlantic and rake all the money in", it might be worth going for it. Huge empires have huge trade potential, so going for trade and naval ideas (especially for thassalocracy) seems to me to be worth it. The only problem with a capital in sevilla is that you'll need a land connection through Hungary, Austria, Venice, Italy and France to keep everything from turning into colonies, though that shouldn't be a problem. Now that Sevilla is an end node, Antwerpen is nowhere nearly as precious as far as I can deduce. So as for Europe, my suggestion is to make the mediterannean your private pond. You do need Bordeaux for Thassalocracy though, so you might wanna expand further into France, preferably while there is a good number of French vassals to go around too. This also restores Rome to its largest borders if you've been taking land in Africa as well, pretty much, so that's pretty neat.
Do note that cores take twice as long to expire if a country doesn't exist; so if a core that looked like it would expire in 1644, that will revert to 1544 when you release the country as a vassal and thus will expire at the end of the month if you are in your second century of the game. Here's a workaround:
1. Acquire at least one core of every country you wish to release as a vassal, as you normally would.
2. Wait out the truce, coring the provinces if overextension can burden you.
3. Release all those vassals at the first week of a month, then declare war on the holder of their cores (in this case France) immediately. Now that they are at war with the holder of their cores, that core timer will reset from 1444 to the current date.
As for allies, you don't really need them, but France would help with Spain and Portugal quite well, so you might wanna keep them around until you take their slice of the mediterannean. Russia has already been nerfed and if you've cut them off, they'll probably never grow to be a substantial power. Although, they might be PU material if you wish to bother with it, but PUs are too uncertain. You will probably be fighting Britain and the Iberians for trade and colonies, so that's all you've got.
As for ideas(those in parentheses are potential picks);
Admin:
(Innovative)
Religious
Administrative
Diplo:
(Trade)
(Naval)
Expansion
Military:
Defensive
(Offensive)
(Quality)
