Where can I store cars that I find?

You can store cars in the garage at any crib, and at any Rim Jobs. Cribs show up as little house icons on a yellow background. Rim Jobs are green icons with wrenches on them.

At the start of the game, you'll only have access to Shaundi's Ex's Loft as a crib, but complete more story missions and more will open up to you (as Ashley list indicates). Some of the cribs have helipads, and these store air vehicles such as choppers, and later... well, I don't want to spoil it ;)

You can buy Rim Jobs locations, but this is not required to store cars or access your garage. This just allows you to lose your wanted level if you enter it, and gives you a "periodic income" boost. You'll be taken to a Rim Jobs location early in one of the plot missions, but they are located across the city and are unlocked from the start. Rim Jobs locations can't be used if you have a wanted level, unlike crib garages which work regardless of your wanted level.

If you invest any money in a car, it becomes yours permanently unless you delete it from your garage - you can lose the car, destroy it, drive it off a cliff into the river, etc, and it will always reappear in your garage shortly afterwards. Under certain circumstances you may have to pay a $500 fee to recover a car that's been lost or destroyed.

You can usually store cars whenever you wish, so long as the car isn't required for a mission. There are times when you can't access the garage, and the game will tell you so if you try to approach it.

When it comes to what can be stored - if it is a land vehicle, and you can drive it, you can store it in any garage. You might not think you can fit a tank inside Shaund's Ex's Loft, and it's a little bit of a squeeze, but it fits :)

In addition to the "land vehicle" garages, and helipads at certain cribs, there is also an airplane hangar at the airport you can buy, and a boat dock or two if you wish to store some boats.

Here is a list of cribs from the Saints Row wiki:

In Saints Row: The Third, all but two Cribs are acquired through the completion of missions; Rondini's Boat Dock and the Airplane Hangar are available for purchase at anytime after completing the third mission of the game, "We're Going to Need Guns". Cribs can no longer be upgraded like they could in Saints Row 2, although Safeword, Burns Hill Reactors, and 3 Count are considered Strongholds as well as Cribs, and are thus upgradable.

• Shaundi's Loft (unlocked after completing "We're Going to Need Guns")
• Saints HQ (unlocked after completing "Party Time")
• Angel's Gym (unlocked after completing "Return to Steelport")
• Kinzie's Warehouse (unlocked after completing "Return to Steelport")
• Zimos' Pad (unlocked after completing "Return to Steelport")
• Safeword (unlocked after completing "Pimps Up, Hos Down")
• Burns Hill Reactors (unlocked after completing "Stop all the Downloading")
• 3 Count (unlocked after completing "3 Count Beat Down")
• Rondini's Boat Dock ($12,500)
• Airplane Hangar ($15,000)

You can also store your cars at the Rim Jobs garages.