battlefield movement control

[MercCpt]

Hey all me again trying to craft a character that can do a few things and my ideas are clashing so here I am asking you all for advice!

What I want to achieve -
1. Freely move across any terrain in a battle (ignoring difficult).
2. Use either 3rd lvl swashbuckler or mobile features to maneuver around enemies.
3. Either use relentless hex (Eldritch Invocation) or some form of teleportation to catch up/surpass enemies.
4. To not rely on racial flying to game the system.

So far that's about it I realize monk can do most of this but in my opinion monk sucks so trying to avoid it if I can.

[Houster]

Hey all me again trying to craft a character that can do a few things and my ideas are clashing so here I am asking you all for advice!

What I want to achieve -
1. Freely move across any terrain in a battle (ignoring difficult).
2. Use either 3rd lvl swashbuckler or mobile features to maneuver around enemies.
3. Either use relentless hex (Eldritch Invocation) or some form of teleportation to catch up/surpass enemies.
4. To not rely on racial flying to game the system.

So far that's about it I realize monk can do most of this but in my opinion monk sucks so trying to avoid it if I can.

Mobile takes care of the first two, misty step the third(spellcasting, fey teleportation and fey touched(if in tasha's) or dimension door(spellcasting). The fourth- just pick any race.

So you have a ton of options. If you like to run fast, take tabaxi. If you want A lot of misty step and being in the frontline somewhat- bladesinger.

But really there is a ton of options.