I've just started a new game, and because I'm not doing the MQ for a while, I'm lacking a house to put stuff in. Are there any good player homes that are free and have a few non-respawning containers. Preferably near a fast travel marker as well.

I don't care if its a cave or something, I just need to put some stuff away.

Here is some info from the WIKI

Free Shacks

There are several empty shacks around Skyrim, many of which contain a bed and at least one http://www.uesp.net/wiki/Skyrim:Containers#Safe_Containers, making them useful as a home until you are able to purchase one:

• http://www.uesp.net/wiki/Skyrim:Alchemist%27s_Shack, near http://www.uesp.net/wiki/Skyrim:Ivarstead, has an end table that is safe for storage. It also has the benefit of an alchemy lab.
• http://www.uesp.net/wiki/Skyrim:Meeko%27s_Shack, west-northwest of http://www.uesp.net/wiki/Skyrim:Morthal, has an end table that is safe for storage. The barrel and shelves respawn, however, regularly filling the house with junk.
• http://www.uesp.net/wiki/Skyrim:Riverside_Shack, southwest of http://www.uesp.net/wiki/Skyrim:Windhelm along the http://www.uesp.net/wiki/Skyrim:White_River, has one safe wardrobe and a bed.
• http://www.uesp.net/wiki/Skyrim:Abandoned_Shack, east of http://www.uesp.net/wiki/Skyrim:Solitude, will remain accessible after you complete either of its associated quests. It contains an unowned bed, but no safe containers.
• http://www.uesp.net/wiki/Skyrim:Traitor%27s_Post, east of http://www.uesp.net/wiki/Skyrim:Windhelm, has two wardrobes and a cupboard that you can store items in. The chest there respawns along with the bandits.
• http://www.uesp.net/wiki/Skyrim:Lund%27s_Hut, north-northwest of http://www.uesp.net/wiki/Skyrim:Rorikstead, is a farm house with a non-functioning bed. Only the chest and end table are safe containers.
• http://www.uesp.net/wiki/Skyrim:Anise%27s_Cabin, southwest of http://www.uesp.net/wiki/Skyrim:Riverwood, can become a good early-game base of operations, although it is initially occupied. See the article for details.

If you make friends with either Faendal or Sven, you can take the key to their house. Generally, end tables and cupboards don't respawn, so are safe to store things in. I prefer Faendal, as he lives alone.

Or, you could join a guild. If you're a warrior, try the Companions, a mage: the College of Winterhold, a thief: the Thieves Guild, an assassin: the Dark Brotherhood. For all of them, you get at least one non-respawning container and a bed you can sleep in. The Companions are the most central, in Whiterun.

If you don't want to join a guild, you could try http://www.uesp.net/wiki/Skyrim:Anise%27s_Cabin. It's right near Riverwood, and ideal for a mage character, as it has access to an arcane enchanter and an alchemy table. You can also fast-travel there. If you go in the basemant (where the crafting tables are), she'll attack you, but if you kill her, you can sleep in her bed. The end table is always safe to store stuff in, but the barrels outside respawn.

On edit: Ninja'd!

Some I've used (all with FT markers):

Alchemist's Shack in the westernmost part of the Rift (just after walking the mountain pass from Helgen). Completely free. The end table is safe and you can use the bed. Barrels and open surfaces respawn.

Riverside Shack south of WIndhelm, along the river. You'll need to kill a bear, and to pretend you don't see the remnants of the former owner on the floor. The wardrobe is safe and you can use the bed. Chest and open surfaces respawn.

Anise's Cabin close to Riverwood (on the other side of the river). You'll need to kill Anise first though - either just attack her or break inot her basemant first, then she'll attack you. You can use the bed, the entire basemant is safe. You can also use the cupboard and dresser on the ground floor (I've tested, things you put there shouldn't be marked as stolen, but you can always test for yourself if you're unsure). Barrels, sacks, and open surfaces on the ground floor respawn. There's also a small garden, which will respawn.

Another quick way to get a house is to get married to some house owner. I believe Ysolda and Uthgerd are popular choices since their favors are easy and they have houses in Whiterun.

More safe locations can be found http://uesp.net/wiki/Category:Skyrim-Places-Safe.

Edit: ninja'd.

On the guilds... Bard's Guild svcks! No bed to sleep in. No place to store your things (I think, but could be wrong here).

I don't consider that one a guild, which is why I didn't mention it. You don't actually become a member of the faction, can't live in their HQ or store your stuff there, and they have nothing resembling a questline, only one main quest and 3 dinky little sidequests.

Good points. It is a Guild in name only

Thanks for the suggestions. I'll be sure to check them out!