I won't rehash the smithing threads. Indeed, smithing your own weapons is probably the best answer. But let's strike that for the present and list a few ideas for new players to find decent (cheap?) weapons early in the game.

I'd say the best source of decent weapons is Drauger tombs. The regular draugr weapons are ok and dirt cheap (so not so good for gold accumulation) but they work very well. Occasionally, you'll find a "honed" version of the weapon, and that is the one to grab. it makes a great weapon to start off.

Another possiblity is to start the Companions quest. One of the first fetch quests is taking one of the Companion's longswords to the forge for improvement. Keep that for a while. It's free and skyforged steel is a great material, especially early.

If you go a little further in the Companions quest, you'll be somewhere with Farkas and he drops his skyforged greatsword. When you see him again, he has it yet the dropped one is still there. Pick it up and you have a great two-handed sword.

Along that same path, if you complete the companions quest, you can (possibly depending on your smithing) forge hero nord weapons from Drauger weapons, and those are almost up to Ebony and Daedric.

Lastly, doing the Thane quest for a hold (Whiterun is the easiest and it's early on the main quest line) gets you the Blade of Whiterun (though what this actually is varies wildly. But it can be a good starting weapon.

More ideas?

Bolar's Oathblade was pretty easy to get. Take the path to the right, and take it back to the entrance after you get the sword, and you only face two Sabrecats, one bear, and one Spriggan. Health pots can get you through that, even at low levels. I killed one of the cats from the cave entrance with a bow before he got to me, and had to fight the second melee. The bear was a little harsh, but use the terrain to your advantage and it can be done even at lower levels.....

there is the castle tower on the way to Invarstead, SE of whiterun, where bandits will stop you.

there is always a magic bow there at the top of the distant tower on the table.

you could always run through the companions quest really quick and get the skyforge sword. I think you get it after going to dustmans cairn with farkas in the very beginning of the questline
LOL I did not read the OP