If I reroll 3 skins of the same type, say 3 legendary skin shards, will I get a different legendary skin shard, or literally any random skin?
I couldn't find any offical FAQ answer on this, but obviously rerolling 3 legendary shards does not automatically result in a permanent legendary skin. Here's a counter-example where the player is rerolling Alpha Battle Skarner, Battlecast Prime Cho'Gath, and Project: Yi (all of these are legendaries) and it gives a permanent Dragonwing Corki (regular permanent skin).
Also, this reddit post and LoL Boards post tell that rerolling skin shards is random. You can get a 520RP skin from 3 Leggy's and vice versa. This is, of course, all experience-based, but finding counter-examples is enough to answer this question.
So my advice would be to disenchant high-value skin shards into orange essence, and to reroll the low-value skin (520 and 750RP) into permanent skin.