This is my first time posting on here so I'm not 100% if this is the right place to do it but oh well here we go

I'm re-making a character I had lined up for a campaign that was unfortunately postponed (thanks coronavirus) and I've decided to completely re-do it. I was thinking it might be fun to make a caster who mainly uses teleportation stuff, kinda like a wizard who uses mostly fire-based attacks, except instead of firebolt and wall of fire, I'd have blink and dimension door. Here are the things I'm not so sure about:

• I don't know which class I should use. Most of the spells I've looked at are available for most of the spellcasting classes, so is there something else I should take into consideration when deciding? The character was originally a warlock, so should I just stick with that?
• There aren't too many teleporting spells that are available at early levels, so I wouldn't really be able to say that my character specializes in it until I've gathered a few of them. Anything I can do about this?
• And lastly, I'm not sure if the idea's worth the trouble. It seems cool in my head, but (as far as I know) it's not like one of those sub-classes where the caster focuses on a specific school or domain. 

Thanks for reading, and I appreciate any help y'all can give!!!! 

Conjuration school is where there’s teleporting. There’s even a class ability for wizards for it. (Level 6, lets you teleport and/or swap places with other willing players).
I think it could be a cool idea, you should go for it. Teleporting around the battlefield, or past the guards, has lots of utility, especially when you can start bringing someone with you. And if you go conjuration school wizard, you’ll have some summoning magic and other tricks to supplement and give you more utility. 
Sorcerer or warlock could work, though sorc metamagic doesn’t seem quite as useful with teleporting, and neither class gets many other spells, which would limit other things you can do. 

Well with Distant Spell metamagic you essentially double the range for your teleporting prowess.

Would agree Conjuration Specialist would be overall best fit.

For your early spell choices:

Misty Step is the earliest "teleporting" power out there.  That said Expeditious Retreat is your warm up, Feather Fall illustrates your "mastery of movement", Haste is another "form" of movement mastery.  Minor Illusion to make oneself "disappear" as warm up.  Ray of Frost, as you "slow down" the enemy would be a good cantrip as well.

Quote from Pedroig >>

Well with Distant Spell metamagic you essentially double the range for your teleporting prowess.

Would agree Conjuration Specialist would be overall best fit.

For your early spell choices:

Misty Step is the earliest "teleporting" power out there.  That said Expeditious Retreat is your warm up, Feather Fall illustrates your "mastery of movement", Haste is another "form" of movement mastery.  Minor Illusion to make oneself "disappear" as warm up.  Ray of Frost, as you "slow down" the enemy would be a good cantrip as well.

 I like the way that Pedroig is taking the "Other" stuff. It fits a bit with where my mind went as I was reading the original post, what is the focus that the teleportation fits into the most for the character? Is it the movement like Pedroig took it? My mind went to defensive spells, which took me to Abjuration Wizard (though the teleportation wouldn't activate the ward)? I think that picking that theme and then playing on the theme will develop the character in a way that complements the teleportation "subtheme".

Sticking with Warlock could enable Grasp of Hadar, Repelling Blast, and Lance of Lethargy cantrips for Eldritch Blast. 

Forget all these. A dream druid is where it's at for battlefield positioning.

Take eladrin race for misty step. Like it has been said, dream druids and conjuration wizards are good. If you wanted to be good in combat, then playing either fey wanderer or horizon walker would be a good pick. They get cool teleportation-type abilities at 3rd level.

Quote from KaoshiElder29 >>

Take eladrin race for misty step. Like it has been said, dream druids and conjuration wizards are good. If you wanted to be good in combat, then playing either fey wanderer or horizon walker would be a good pick. They get cool teleportation-type abilities at 3rd level.

 Eladrin get Fey Step, but it's pretty much misty step. Shadar-kai also get a teleport and they resistence to damage when they use that teleport.

Shadow monks can teleport from into darkness and get a few of spells that play well with the theme.

Most spellcasting classes have some subclasses with an ability to get some teleportation abilities (usually through adding spells) so you can choose most spellcasting classes and have options that fill your desire somewhat. 

Shadow Sorcerer does get Shadow Walk at 14. And the classes already mentioned in the others posts are the sum total of classes with actual teleporting abilities that aren't spells.

I'd go Mark of Passage Human as a Conjuration wizard.

I play a Warlock who specializes in teleporting and I love it. The Archfey Patron gives you one of the best teleportation abilities in the game at 6th level, and it resets on a short rest. Misty Escape lets you teleport 60 feet and turn invisible as Reaction. As far as I know it's the only Reaction-based teleport power.

Your spell slots also reset on a short rest. Misty Step, Thunder Step, Dimension Door, Far Step, and Scatter are all on your spell list. (Scatter would be your 6th level Mystic Arcana pick, so be careful with that one.)

What you DON'T get are the long range teleport spells like Teleport, Teleportation Circle, etc. If you want to be a long-distance "utility" teleport expert, choose Bard, Sorcerer, or Wizard.

And I agree, Eladrin would be the best choice for race; having that extra short-rest teleport as a racial ability is too good to pass up.