I've been through this process, too! Here's a few of my thoughts.
- Screw top - never really bothered with these. Many screw tops are quite flimsy, and I've found they tend to leak when retightened.
- Crown cap - (what you call "bottle caps".) When I'm bottling in pints, this is my preferred option. You do need to check, unless you're not using a capper which needs to grip the neck of the bottle, that the bottle neck profile is suitable for your capper. I've even had some success, where I've had to let off excess pressure, lifting the crown cap and then recapping.
- PET - if I am bottling for (say) a party, and don't want to use a keg, I bottle to 2l PET bottles. My experience is that they are easy, convenient, and can be used safely at least two or three times. After a while, though, the appearance of the bottle can begin to deteriorate, and some say that they become harder to clean properly with time, and may harbour bacteria. The biggest problem with them in my experience is that you really need to decant to a jug - repeatedly pouring individual glasses of beer soon stirs up the yeast sediment, and the last pint or so often gets cloudy.
- Flip top - I've never used these extensively, as I haven't found a source of supply that's free (or cheap enough). I do use some 0.75l lemonade bottles, and they are definitely my preferred option.
As far as your manky bottles go, I agree that the biggest problem with brown glass beer bottles is getting them clean. I also find delabelling commercial bottles a right hassle.
What I suggest you do is to use one of your fermenting buckets to hold a good strong solution of VWP (or other preferred cleaner/steriliser) in very warm water, and get your manky bottles in there for a really good soak. I generally fill it about 2/3 full, and put each bottle in individually to fill them up enough that they won't float up. Then, when you've done them all, stack them neatly into the bucket, in more than one layer if necessary - you can top it up with water if you need to.
Leave them to soak for a few hours, assuming "manky" means you've got encrusted yeast deposits on the bottles. Then take each bottle out, part-empty it, and give it a damn good shake with your thumb over the top (a bottle brush is useful, too), before emptying them. If they're very manky, your water is going to pretty quickly end up fairly disgustingly full of bits of yeast and dead mould plaques, so in that case I'd usually give them a second clean in fresh solution, inspecting each one (hold it up to the light and peer down the neck) for any remaining deposits.
Then you need to rinse them, to avoid the chlorine taint, just before you fill them.
It sounds laborious, but I find I can get into a fairly good rhythm, and they get done pretty quickly. It's a good idea, when you're drinking beer from glass bottles, to remember to rinse them out immediately, before the yeast has a chance to dry onto them - then all you need to do is a light sterilise with VWP and rinse when you need to use them next.
It's purely subjective, but personally I find I get a great sense of pride when I bottle a batch to 40-odd pristine crown-capped brown glass bottles - I like the way that they're so clean they almost stick to your fingers when you pick them up.
And, of course, when I'm labelling them, I never use glue so strong that delabelling them again needs any more than a quick soak in warm solution - my glue of preference there is Pritt stick.
If you are reusing swing top bottles, it's worth pulling off the plastic cap from the ceramic top, and giving them a soak in steriliser before dropping them into clean water, taking each one out and reattaching it to the bottles as you fill them. You can get replacement caps when they start to wear or split.