If you're gearing up for 'Vampyre Slayer' in 'Old School RuneScape', the official, hard requirement you need is Attack level 20 — that's the only skill gate you must clear. There are no other quest prerequisites or skill checks to start it, so fresh accounts can do this as soon as they hit that Attack level. The quest itself is short and combat-focused: you'll be dealing with a vampyric foe whose health and defenses make a basic melee setup the fastest way through.
For a smooth run, bring a decent melee weapon (a scimitar or better), some food for a safety net, and decent armour so you don't waste time healing. Teleports or runes that get you close to a major town speed things up, and having a few extra Attack-boosting potions or an extra stamina potion is overkill but nice if you want speed. It's a quick quest that gives a respectable chunk of Attack experience, perfect for early-game training — I always enjoy the feeling of zipping through it and watching my Attack tick up.