Manyu/Dragon
I'm usually running the event maps and if I get done early I will try to farm manyus for the priority girls of the moment, usually I attempt to level efficiently.
I don't try to farm dragons unless I need them and keep a stock of Large and medium dragons (as much as i can for the large and max of 3 per type for the medium).

Seeds/gold
For gold I mainly get it from event maps (80 stam) and use it all the time, if I run out of gold i use the seeds to do a massive amout of summoning (last time i did it i had like 250k seeds).
for the equip seeds i use them when i hit near 8k - 10k+ then hopefully I get lvl 10 gear if not i just use them all on event equipment.

Looking at the replies above, I guess my playstyle doesn't really differ all that much.

General resources
Gold - At the early stages I needed to run through the Saturday special map a few times when I was about to run out of it. The early leveling and evolving knights / leveling equipment drains quite a lot of this resource. Now, when almost all of my knights are evolved, simple runs through the advanced event maps are all I need to not be worried about gold. The 12-5 map, which I run when I don't have anything else to do, isn't bad with its rewards as well.

Gacha Seeds - I've never really farmed them. Early on, each time the amount hit 1000+ I did a pull to get a new 2-4* knight. Now that I have all of those from the standard gacha, I'm not using them and just waiting for when the new 4* knights arrive. Once again, 12-5 can be a good source of gacha seeds.

Equipment Seeds - Just like Gacha Seeds, I've never really farmed them. These are the main culprit to my low gold levels early on in the game, since I leveled every high quality accessories (20 of each type max). Now I'm just storing them and not leveling anything - I'm waiting for when the Equipment Manyu from DMM get implemented into our version.

Girl specific resources
Manyu - Since I level each and every one of my knights I really need a lot of Manyu. I've read through a guide early on and used to run 2-1 and later 12-3 and 12-5 in order to get the Secret Garden run at the end as my main source of Manyu. I avoided the Wednesday and Sunday special missions, since back then they were inefficient to me. The special mission could get me 1-4 Manyu of any level (5, 20, 100) for 80 stamina. The advanced Secret Garden could get me 3-4 Manyu of the 2 higher levels (20, 100) also for 80 stamina, which for me was a better deal. The only downside was the probability of spawning the map, but since I've been running 12-3 and 12-5 mainly, it was not really a problem. Now, when an extra drop got added to the special missions, I think they are worth running and they became my priority on their days, in case I don't need to hurry up with anything else (for example an event).

Dragons - It's possibly the only RNG part of this game that annoys me. I like FKG, because the maps are not really frustrating with their random nodes - it's just luck of the draw with a possible reshuffling of your squads to better the odds and you'll get it eventually. Dragons however have specific days they show up at and a 80 stamina farming map with a really low probability of getting the high level ones. I never farm them if I don't have any knight exactly at that moment to evolve because of the limited storage space (let's hope that the additional 200 DMM storage space will get to us eventually) and it can sometimes take a full day of farming to get enough of them to evolve a 5*. If I get a lvl 100 Dragon from an event I always keep it stored.

Ampies - I used to ignore them early on, since my team wasn't strong enough to get them from the high-end rewards from events. Now I always try to get them from events, even with higher priority than Manyus. They also drop from advanced event maps and later campaign missions (like 12-5) from time to time. I give them to knights that I know will be a part of my team for a long time - 6* or 5* with a great utility ability. I also fed quite a lot of them to Violetta Pansy early on (one of my favourites) just for the heck of it.

Gifts - I remember farming those really hard at one time. There was a 5* ticket gacha going on (the first time I saw one) and I farmed the gift special map to raise all the affection I could to get the FG on time to use the gacha. The reason for that was that just the day before it started I blew 100 FG on priority pulls that I basically got squa from. Now I basically have enough stored to instantly get a new girl of any preference to 100% (and more if that was possible), so I'm not even farming them. These also drop from later campaign maps and gatherings, so I get new ones all the time. These are usually the lowest priority in the event rewards for me.