Stealth is an ability used by thieves, rangers and their kits. It has two uses. First, while the character is hidden, they are invisible. Second, an attack they make while invisible will be a backstab and receive a damage multiplier. For an assassin, this goes up to x7.
Hide in shadows and move silently both contribute to your stealth. Most evidence I can find suggests that your stealth is equal to (Hide+MS)/2. It's also hypothesised that hide in shadows benefits the initial check and move silently has a greater effect on checks to remain hidden. If you want stealth, invest in both equally. Since it's a % chance, 100 in each is enough.
The rest of your thief abilities depend on whether you have another thief in the party. Having at least one character with Find Traps is vital in some areas. A character with high Open Locks is also recommended- you can replace them with a character with massive strength or a wizard with knock but you will miss out on loot this way. You can completely ignore these by having Imoen use these skills instead and ignoring stealth.
Pick Pockets is not necessary. It provides alternate solutions to some quests but involves a lot of reloading when you fail and turn entire towns hostile.
Set traps is interesting and is typically an all or nothing investment. The damage and number of uses scale with level so it's not really worth using in BG1 (especially since you don't have the spare points). Late game, traps can end certain encounters before they start if you can put all of them on top of each other.
See Illusions is another interesting point-sink once you've maxed out your stealth. It gives you a flat chance to automatically remove illusion effects from enemies.