Its so long, since I played alttp, I think skyward sword is the last game I played. So amazing too have a bunch of zelda games unplayed for the future 
I actually started with firebird and imported DoR-tiles to it. I wonder, the Death-Animation in Firebird looks nice, but 8bit tiles are not affected... also, can I mess up cset 6 for the link sprite or is it needed orherwise?
C-set 6 is also used for some items, such as the arrow, bow, and lv.1 boomerrang, and enemies like pol's voice, and like-like by default. You can edit it, but just be sure to include colors for other items/ enemies, unless you plan on changing their colors anyway. Extra Sprite Palette 9 (Quest-> Graphics-> Palettes-> Sprites-> 1, c-set 9) has a copy of the default cset 6 (at least in Classic) so check there, and if there is a back up, you can copy that over your main cset 6 if you mess it up.
If you want to change Link's colors, I recommend finding all items, and enemies that use cset 6, and change them to something else. Then, you can mess with Link's colors. Also, you'll want to keep certain colors consistent with Extra Sprite Palettes 6, 7, and 8 as these are the colors for Link's other Rings (blue, red, and gold respectively). What I mean is, you want his skin, and hair colors to remain the same, if you chang the colors of the tunic/ add/ move colors.
Hope that helps
EDIT: If you don't know, you can change the colors of items and enemies by going to them ("Items", or "Enemies") under the 'Ques't menu. Select the item or enemy, and go to 'Edit'. Here, you can choose a tile, and c-set from the main palette by pressing "+" or "-" while on the tile-select screen. Under 'Enemies', you will see "Old" and "New". This determines the tile, and c-set from the main palette used depending on if the rule "Use New Enemy Tiles" under "Quest-> Rules-> Enemies" is checked. You shouldn't have to mess with the animation tiles if you are using a pre-made set like firebird. Just use "+" and "-" to change the cset. For Items, you go to the 'GFX' tab in the item editing window. Here you can also choose the tile, and cset from the main palette to use for the item. Make them not c-set 6, if you want to fully edit c-set 6 (Link's cset).
As for bad chosen palettes and such, that's only personal opinions, but a quick tip, make sure the palette you choose has a bit of "logic" as to why you are using it. A quick example: say you were to design a graveyard area. A bad chosen palette would be a happy and colorful one, wouldn't it? I would go for gloomy and spooky colors that blend in with the atmosphere of a specific area. 
