This all comes down to ruling
When does combat start? The rules do not say so explicitly, so this will be for the DM to determine. A good proxy to start combat is when anyone tries to take any combat action (e.g., tries to make an attack). This works with standoffs, traitors, and trying to ready an action before combat (which as a combat action starts combat and avoids the issue). Spellcasting such as teleport however is not necessarily a combat action.
Once combat starts, you follow the rules under Combat Step by Step (PHB, p. 189):
- Determine surprise. (...)
- Establish positions. (...)
- Roll initiative. (...)
Who is surprised?
Who is surprised is entirely up to the DM (p. 189, PHB):
The DM determines who might be surprised. (...) Any character or monster that doesn’t notice a threat is surprised
The Sage Advise Compendium elaborates further what is meant by "notice a threat":
you must be caught off guard, usually because you failed to notice foes being stealthy or you were startled by an enemy with a special ability, such as
the gelatinous cube’s Transparent trait, that makes it exceptionally
This expanded definition is valuable, as it shifts the focus from being able to notice a threat to the more general question if you were prepared for the threat to happen. The wizard with teleport materializing suddenly° out of nothing sounds like a good fit for an "enemy with a special ability (...) that makes it extremely surprising".
The caster's team are not surprised -- they may be if they find the room empty or someone else there than they expected, but not in the capital-S Surprise sense where they are unprepared to face a threat or engage in combat.
If the foes are surprised depends on what they expect, not just if they can notice you. If they are unprepared for an attack, lounging around in their den, then they surely would be surprised to suddenly face a group of adventurers out of nowhere. But, if they had some reason to expect the attack any minute, and knew they face spellcasters who can teleport or walk through walls, they might be extremely alert, ready for anything, and not be surprised, even if you teleport in. In most situations however, facing someone who teleported in unexpectedly could be a Surprise.
If the DM rules that casting teleport starts combat, they first determine surprise. The positions are in entirely different places, so unless the foes await an imminent attack or have special abilities like Alertness or the Foresight spell, they have no indication yet of anyting and are near certainly surprised. All roll initiative. You use teleport as your action in the surprise round and only those of your group with lower initiative count or with readied actions can act after teleporting. This case is weird because if you have a teleport mishap, you never get to combat.
Starting combat when you arrive is the more natural option. You teleport, the DM determines surprise, the DM declares where everyone stands, all roll initiative, and the first combat round begins with everyone acting on their count (or not, if surprised). If the foes are surprised, this option is more lethal, as your whole team gets a full round of unopposed actions.
Readying teleport pre-combat to gain your action in the round where you teleport would only work with a maximally lenient DM, as the Ready action is a combat action.
Any group with access to Teleport very likely also has access to Arcane Eye and Scrying, and will be able to employ unbalancing "Scry and Fry" tactics.
If teleporting by default is surprising, such a group reliably can get the drop on unsuspecting foes and slaughter them, especially if you use the interpretation that combat starts when they arrive, giving all of them full actions. (Ruling combat starts on teleport at least removes the caster's action and relegates those with higher initiative to readied reactions).
If the group are the PCs, this may be fun the first few times, but runs the risk of becoming boring like any overpowered, repeatable tactic. What's worse, this cuts both ways. If the group are the bad guys, a DM sending in a squad of high level murderers with teleport can easily TPK the Surprised party.
So, from a game-play experience it may be wiser to rule that normally teleporting does not cause surprise, even if it may be less believable.
° All the common teleportation spells have a duration of instantaneous, and the PHB informs us that for such spells its magic exists only for an instant. So we can assume that teleporting is not like beaming in Star Trek, giving others ample time to observe something is going on. It is, by the dictionary "happening immediately, without any delay".