Question: In my story, there is a character that is capable of using magic or an ability that allows them to "teleport" as long as they are in contact with the ground or the area that they want to use it on with at least one hand.

For example, in the middle of a circular arena 100m in diameter, as long as they are touching the floor (with a hand), they can teleport anywhere as long as it is "connected" or still physically part of the arena (which means that any floating rocks won't count, and they wouldn't be able to use it to get away from the arena in the case that it is floating).

What limitations can be set on it to avoid being too powerful, and with limitations in mind (or not), what would be the best type of magic/ability to use with it? (disregarding earth magic/manipulation)

My thoughts were to limit it to 75-100m and only usable every second or two, and to be used with wind magic mainly (if mist or fog can be made using wind magic).

Answer: 
### "Electrical magic"-based teleportation: requires a conductive path.

Suppose your teleportation magic makes your teleporting person act as a self-propelled surge of electrons. As long as they are in physical contact with a conductive surface or conduit, they can teleport to any other point on it with enough space for them to materialize at the other side.

This would impose pretty strong limitations on general use.

* Most dirt/rock/concrete and other surfaces one could stand on would not be immediately usable.
* Bodies of water and wet surfaces (eg. during/after rain) would be easily traversable.
* In urban settings, perhaps a likely use would be teleporting around the electrical grid between points of exposed wiring.
* To use it in non-conducting settings, the teleporter would probably carry coils of wire with throwable weights or a grapnel gun, or perhaps something that splashes water, to deploy in the field.

If you want to impose limitations based on frequency, you can consider heat generated by the teleporter's passage through the medium. If they teleport across a thin film of water on pavement, perhaps the heat of their passage would evaporate too much water for them to take the same path back. If they teleport through a normal circuit in a suburban home, perhaps they'd set off the breaker and not be able to go back through that line.

Related to this, you could add a limitation that they must know, ahead of time, where they are going to rematerialize. Perhaps in electron-surge form, they cannot perceive the world outside of their conductive conduit--at risk of death or severe injury, they must be certain they are re-materializing in a place with sufficient room for their body.
First, you already limited the most unfair application by limiting it to ground use :
The dropping someone off in space and coming back.

This was also only usable if you allow forced teleportation of others. Which you can limit (maximum weight, maximum volume or needing the consent of other living beings to move them)

What you were going for in your thoughts as limitations are frequency and range. And those can be linked to have an adaptive cost:

* Teleportation can take time to prepare and the longer you prepare the farther you can go. For example, by preparing 1 second you can just teleport 1m away but if you prepare 1 minute you can move 100m in one go.
* If you need reflex teleportation, you can reverse the relation to time and instead of preparing you have a cooldown during which it is impossible to teleport after teleporting.

You can also make a limitation on precision. The farther you go, the less precise the teleportation is, which could be dangerous depending on how teleporting in a wall is handled.

As for what magic to use in addition to it, I don't see why that'll be necessary, adding anything in addition to teleportation is already overkill.

You thought of Earth Magic manipulating the ground and changing what's accessible, but that's true for any magic creating/manipulating solids (Ice at least and Plants if you allow teleporting through living beings). Now if you really want to add magic, there are a few kinds that works well with it:

* Any Illusion Magic that makes it seem you didn't move yet
* Any Stealth Magic that allows to teleport undetected
* Any long range Magic that allows Hit&Run tactics

If you want another magic, that seems to combo well but still have limitations, any other contact-based magic will work well.