So, I've been thinking - can I make something like first level Celestial Sun Elf-wizard in a non-homerule non-Dragon Magazine game from the start? Are there any templates that can be applied at the character creation and if there are, which ones are? Especially the ones I don't need to beg my DM for?
If it has a Level Adjustment, it is intended to be playable
Creatures and templates that cannot be played (according to Wizards) have LA: —. Any actual numerical LA (LA: 0 to LA:
Unfortunately, most LAs are much higher than they really should be. Wizards allowed it, but apparently wanted to discourage player use of these things by overcharging for them.
And even if it is on some level “worth it,” it’s very difficult to play with an LA higher than 1 or 2. Even those can be quite problematic, for you and the game. And many DMs don’t like templates for a variety of reasons. So definitely ask your DM about it.
Celestial has LA: +2, and therefore you usually can use it. If you do, you are two levels behind at all times: not even remotely worth it, in my opinion. DR 5-10/magic isn’t worth much: most threats have magic weapons. Darkvision is easily obtained via racial quality, spell, or item. Items and spells can also handle energy resistances. Spell Resistance actually hurts you more than it helps you, in my opinion: you have to spend a Standard Action to lower it if someone wants to heal or buff you. And Smite Evil isn’t very useful to a Wizard, not that it’s particularly useful to anyone when it’s only once per day.
If you want to play a sun elf who is a native of the Celestial Realms, just ask your DM if that’s an acceptable backstory for a character. You don’t need to hurt yourself with this template just to have a backstory.
You can without any issue (besides DM approval) if you are starting at Level 3. Since the Celestial has a +2 ECL. This means that you will start with one class level (e.g. Wizard, Bard) and 2 "effective levels" of Celestial.
You would get all of the stats that a Sun Elf gets in addition to the details listed in that page.
This isn't ideal as it means that you trade Level 2 and 3 abilities for the special qualities of a Celestial:
This might be worth it, but it could also cause complications and for you to be weaker than the other players in some areas (but potentially be stronger in others).
So talk with your DM about it and see what he says, but it is RAW and completely legal for you to do.
Keeping in mind your comment on the original question:
The answer, then, is simple and short: No, you can not.
Dragon Magazine issues (Or wherever you found the "funny templates") are generally not considered rule books.