A note beforehand- This perk tree is actually of debatable value.  There are tons of lockpicks to be found everywhere in Skyrim, and most stores have a few lockpicks in stock at any given moment for a very low cost.  It’s easy to wind up with over 100 lockpicks in your inventory before you even reach level 20, and if you have the patience and spatial reasoning to pick each lock within two or three picks regardless of difficulty, then you mostly won’t care about the Lockpicking tree at all.  As a good guide, don’t take anything from Lockpicking until you reach Ivarstead, and then go check out the burial mound there.  In that dungeon is a Master level lock on a door that bars you from a single chest.  If you can pick that lock with less than four lockpicks, then you don’t need to worry about using the Lockpicking perks to improve your capabilities- you’re good enough to open anything without it (you also get a massive boost to your Lockpicking skill that’ll make picking things easier anyways).

Novice Locks-

Easy locks are easy.  And this makes them even easier.  Not important.  Only take this to get to other perks.

Apprentice Locks-

Slightly less easy locks are still easy, and now they’re even easier.  Again- only take this to reach other things.

Quick Hands-

The first actually useful perk on this tree, this is great for getting into homes- but keep in mind that it does not in any way prevent people from noticing you in their house or taking things that don’t belong to you.  There are a few quests that you’ll want this for (Wylandria’s Items, for instance) where you’re not actually going to be stealing anything, but for the most part this is essentially a ‘for fun’ perk unless you really are a sneakthief.