No-brainer ideas i personally pick for most countries:
1) Administrative: Well, you don't really need half the bonuses, but the second idea of -25% Reduced Core Cost is just too good. Can just unlock the first two ideas to get this one and leave the rest.
2)Diplomatic/Influence: Diplomatic is good in general with cheaper province warscore cost, huge discount to Warexhaustion reduction, additional diplomat... while Influence is better for vassal-heavy play: cheaper vassal integration, increased vassal forcelimit contribution, increased vassal income and some generally useful stuff. (Can be switched for Exploration if you plan on colonising/dislike vassals. Actually, thats what i'd do for Mamluks going for Africa because of all those empty provinces and expansion shortcuts unlockable by colonizing)
3) Religious/Humanist: Group chosen based on your country's own ideas and your religion's possible amount of missionaries. For religions like innate tolerance bonuses and no bonus missionaries like Fetishist, you'd pick Humanist. In case of the Sunni Mamluks, who can get many missionaries via conquest (Rome, Mecca+Medina, Jerusalem...), you'd pick Religious. One of those is instrumental for keeping your country relatively stable and free of corruption from low religious unity.
4) Quantity: My favourite military pick. Although not making your army stronger directly, it makes it much more sustainable because of huge bonuses to manpower, attrition reduction, less upkeep... While also giving a whooping 50% forcelimit increace as a finisher. Besides the obvious bonus of having a larger army, it also gives you weight on the diplomatic stage, as other countries start respecting/fearing you more just because your army is large. Although sometimes, for countries that can easily stack a particular quality bonus, i'd go for other military ideas. Example: France with its Elan giving 20% moral. can be made much more lethal by picking Defensive and unlocking its +15% morale idea for the awesome +35% morale bonus in total.
After that - ideagroups of your choice. most often it will be stacking all the other military ideagroups for wiping the floor with the AI's guts even more

I hope that helped!