No, there's no shelf life on gas tanks, unless you count the lease on them running out. If you buy the tanks, then you are responsible for getting them hydro-tested every 10 years. Which is a sort of expiration date. This is one up side to leasing. Your local welding shop assumes the responsibility for testing their leased tanks.
Store them vertical and in an open space, not in a closet or other enclosed area. Use chains to secure them to a sturdy wall or buy collars for securing them. If you need the tanks mobile then buy or build a good cylinder cart.
If you're going to comply with OSHA, then you need to remove the regulators and cap the cylinders if they sit idle for more than 24 hours. Flammables and oxygen need to be 20 feet apart or seperated by a 5' tall fire resistance barrier(rated for 1 hour). There's lots of folks that don't meet either of these two requirements in day to day activity. There are other regs that you can review at
www.OSHA.gov.
Tanks can last a fairly long time for occasional use. I carry medium sized acetylene and oxygen cylinders, and they last months between fillups. Victor/Harris/Smith have guides that will tell you the fuel and oxygen consumption for various heating/cutting/welding attachements. Estimate how much welding you're really going to do, and then check the equipment companys' charts and calculate how long your tanks will last. Size your tanks accordingly.
Keep in mind that heating and welding use approximately equal amounts of oxygen and acetylene. But cutting will consume 4 to 5 times as much oxygen as acetylene. So if you plan to do a lot of cutting, get a bigger oxygen tank than acetylene.