Well, my method of spy is normally the same as yours, Cloak and Dagger with the Saharan Spy set. Works beautifully on defense on payload or sometimes CP maps. Other times, I switch it up, using enforcer and either stock or spycicle (depending on amount of pyros/availability of health packs), and I'm trying to get better with ambassador.
How to use different watches is another thing.
The stock watch (or any reskin of your choice) is great for a front lines spy. Use it to get behind enemy lines or to make a stealthy retreat. You should always watch for dropped ammo when stealthed, as it can last quite a while, but if you want to sit around, that's good for Cloak and Dagger.
The Cloak and Dagger is pretty neat. A fast recharge and being able to stay cloaked indefinitely means you can camp, retreat a bit and stay in the shadows, and come out when the time seems right. Stab a few dudes and shoot some more, then go back to a hiding spot.
The Dead Ringer is a challenge to pull off correctly, as everyone expects a DR spy, and has learned how to deal with them. The trick with this is to take a hit or two, and act like you're retreating. The Dead Ringer really is great for spies that can act well. Like the stock watch, you can pick up ammo to make your cloak last longer, and the first few seconds of cloak reduce incoming damage by a lot.
On to knives. Generally, the stock knife is a good solid knife with no downsides, and no gimmicks. This is your go-to knife for all-purpose use. The next option would be a Spycicle. Not the best option, but if you're in a situation where you can sit and wait for a knife, or shoot your way out, go ahead and take this pyro-protection. Another good option is the Kunai. This little bugger is great for making a stab, and tanking some damage while you shoot out, then you can cloak away with your watch of choice to stab again. Of course, there's a problem if you can't get behind someone, as you only have 60 life to start.
Guns are so underrated by most new spies, just chose one you like, but generally le'flappydoodle (too lazy to attempt spelling) and the Diamondback are avoided. Ambassador is deadly in the right hands, the enforcer is deadly in even more hands, and the stock revolver is great if you need to do 120 damage faster than the enforcer's two shots.
Spy is about espionage as well. Point out low health team members, find out what loadouts are going down, like kritz or uber on the medic, and possibly what dangerous fellows are in what positions. Sapping is another thing you can do, and it's best to do it with your team to provide some extra firepower to make sure the stuff goes down nice and tidy.
Acting is all about making people you're doing something, but you're not. Like run to a health pack while cloaking, and when fully cloaked, go the opposite (or some other clear and unpredictable direction) way in order to buy some time and throw off spycheckers. Feigning with the deadringer needs to be believable, so take a hit or two if you can afford it, and make it look like you're actually dead instead of taking fall damage and cloaking just to be invisible.
For sappers, really it's a matter of prefrence, and possibly how much teamwork you have. If you have a pesky engie nest and you can't get the engie down yourself, bring out the red tape to stall the engie, and possibly have your team shoot down the sentry/nest while it's busy un-building itself. If you can get the engie down or far enough from the sentry, the stock sapper is good, and a few shots from your revolver will speed up the process.
And for scouts, generally it's good to avoid them, as they're nasty, but easily taken down by your other team mates. Remember, this is TEAM fortress 2, be a team player, point out the scout to your team, and they'll be sure to take it down at some point. Since scouts can do a lot of damage close range, you're pretty dead if they get good meatshots on you. And dealing with pyros is a matter of mind games. Know where health packs are if you see a pyro, and be prepared to go for one. Try to cloak and get around him, or have a team mate take him out. If you can, and he's at the back of the pack, take the pyro out before killing other enemies.
And lastly, know how to play against spy. Be in the mind of your enemy, think as they would think. If you were them, what would you do?
There's probably things I forgot, and things I'm somewhat wrong about. This is all just from my experience, but also, if you're maining spy, don't insist on being spy if there are 5 spies on your team. Switch off, especially if you're on top of the scoreboard. Sometimes it seems the lower-scoreboard people copy the top few guys, so spy will be open in a bit if you choose something else. Lastly, have fun, make your own ideas based on experience and playstyle, because not everything I said here will be true for everybody's way of playing spy, and have fun again.
TL;DR The sun's coming up, it's time for me to go to bed, and I don't quite know what I typed, so I couldn't summarize it without reading it myself
