Have you done any research about effects? I am surprised because there's so much info on the net that you could easily search on google.
Well, anyway, time based effects are usually referred to ones that use delay. These effects include: delay, flanger, chorus, and probably some more that I am forgetting but those are the most popular. Phase should not be considered a time based effect since it uses "phasing" to make the effect (you can almost replicate a phaser with a pickup selector switch on your guitar by just going back and forth while playing).
I suggest that you buy one of those zoom cheapie effects processors so you can see and use all of the effects that you are asking about without actually investing a lot of money. I know many will disagree but seeing your position I think it would be hurtful to buy 1 pedal and then start gassing over other pedals. You've made it clear before that you are undecisive so you should also consider that part when buying something. Another thing to check out is the Behringer Vamp 2 which you can bypass the modeling function to just use the effects. This also makes for a great lightweight backup.
There aren't any rules for running effects and you will get ten different responses from 10 different guitarists. Sometimes it's better to learn the hard way because you tend to learn out of necessity instead of someone giving you their biased opinion.
With all of that said the first pedals I bought were a Boss Bf-2 flanger and an MXR phase 90 phaser. They were pretty cool at first but I never found a practical use for them. Now I am nearly effectless and don't feel the need to have any effects. If you've made it this long without effects you probably don't need them and may never wind up using them. The one thing I do have is a Behringer V-amp2 that i can use as verb, delay, flange, chorus, phase, compressor, tremelo, rotary speaker, and auto wah for my Triaxis. That would probably hold you over. The vamp2 is extremely easy to edit on the fly since it's like having a pedal with knobs right there(because it actual has knobs with lighted position markers). The effects are decent enough to use live but might not cut it in the studio.
Good luck.