Next thing you'll do is go into swamp, so you may as well enter a bit early and get some of the fruits of the swamp. The only thing The Elder gives you is the key to get into the crypts and get iron, which is great, but there are other things there that will make the fight with The Elder easier.

1) Look for the yellow flowers, which are turnips. These will allow you to upgrade your cauldron and make better food.

2) Kill some Draugr and get some guts to make sausage.

3) Kill some leaches to get bloodbags to make black soup and/or blood pudding.

3) I think you can make more advanced mead with other swamp items.

In the fight, I like to find a ruined tower nearby and fortify it a bit. Make a higher-level spot to shoot from where you can have some stone walls protecting you. Kite him that way and fight him with some protection.

If you have high health before the fight, you can get quite a few melee hits in before you get beaten down too much. As others have mentioned, an axe works. I prefer sword, which works pretty well with the secondary attack. Get as much damage in before your health takes too much of a hit and then run for the tower to finish him off.