Good bows and armour at the start of the game?

yes,first when you get to explore the world,first thing you see are wolves,right? kill em' and grab their pelts and keep on hunting and killing wolves for their pelts. Then,go the nearest town with a forge and a tanning rack,make some leather and make some of those into leather strips BUT leave some leather then make your own set of leather armor. And i dont know much bout' bows .or if ur playing on the PC,you can download mods

Thanks for the info the_FAMAS_pro and DarshD!

If you have the coin, try 'Castle Fletcher' in Solitude, it's next to the Blacksmiths.
Alternatively talk to the Khajiit caravans, both of these generally have higher level bows.
If you want a huge challenge at lower levels, try Lost Valkygg http://elderscrolls.wikia.com/wiki/Lost_Valkygg
The fight here will be very tough against a Draugr with an Ebony and arrows, so bring a follower. However if you kill it and get that bow, it should last you for almost all of the game.

The companions headquarters in whiterun - there's a good elven? bow in a glass case.

quote BluePhoenix

Taking that is stealing though surely?

Yeah, and you have to wait for Kodlak to go to sleep. He won't, unless you join the Companions, but there's also a Daedra Heart I usually take for The Cursed Tribe quest. Enchant it to remove the Stolen Tag.

There's a good one in the middle of the Dark Brotherhood questline. When you go to the wedding, there's a door to your left (with your back to the happy couple) that leads to a balcony. A few Elven Arrows up there too. If you give 1 to an Archer Follower, he'll keep shooting them, and you can loot more from the bodies. Because of the few neccessary kills in the questline, you can get to this point at real low level by bee-lining for it.

When you get to Riverwood, look for an Elf (the only one in town) do a favor for him, and tell him "Follow me." He'll train you up to 50 in Archery, and you can Trade with him to get your money back. They patched the pickpocket training exploit, but left in this Disk 1 Nuke. Also, if you spend 7 level points on Magika, you can buy Bound Bow from Farengar Secretfire in Dragonsreach, or find it in Fort Amol prison. I warn you, this can ruin a character in so many ways, but it can do Daedric damage before level 10, comes with free arrows, and can't be Disarmed. (It'll eventually make you a Conjurer, if you use it too much, though.)