Minecraft Wiki has a table of damage done by weapons.
Swords: The best ordinary weapon (by damage numbers) you can readily make is an iron sword, and the second-best is a stone sword, which is very easy to craft since it only requires wood and cobblestone.
Bow and arrows: I strongly recommend keeping a bow and arrows, if you can, because it enables you to kill monsters at a far distance (especially important since spiders jump at you and creepers will explode without actually touching you). A bow requires three string and three sticks, so the hard part is killing enough spiders to get the string. You could:
•Kill spiders in the morning, when they will only attack you after you attack them and so won't swarm.
•Build a trap for wandering spiders; for example, a wall of cactus which you're on the other side of. However, this isn't as easy now that spiders can climb; you'll have to put an overhang on top so that they climb up it and stop.
•Or just kill spiders with your stone or iron sword.
Arrows for a bow are made from flint, feathers, and sticks, or are dropped by skeletons. Flint is readily obtained by mining gravel (any gravel that doesn't produce flint can be re-placed and mined again for another chance at flint), and feathers may be obtained easily from chickens.
Burning: It is possible to set enemies on fire, but it doesn't kill them very fast. A more practical possibility is to drop a bucket of lava. The safety of this depends strongly on the terrain (you can outrun lava unless you're clumsy, but the real hazard is if the flow blocks you from walking back to pick up the source), but if you can do it then it will bog down the enemies that try to chase you across the lava and kill them reasonably quickly.
Armor: Also, find a herd of cows and start breeding and slaughtering them to make leather armor (24 leather makes a full set). Armor makes you take a lot less damage, if nothing else so you can get in some aiming and timing practice in those beginning fights. Also, killing cows and chickens will help you learn how far your weapons reach and how to aim at a mob.