The only cartridge I can remember that is supposed to be different in dimensions between military and civilian is the 5.56 x 45 / .223 Remington. In the late 1970's or early 1980's SAAMI warned of chambering differences between military and comercial arms that could cause increased presure if military ammo was used in comercial rifles.
I have just run a dial calipre over a number of rounds in my collection, and yes, the neck on military stuff is greater in diameter/thickness than comercial amo, BUT all the rounds I have, including some Vietnam era Remington UMC and more modern military from the US, Australia and europe are all below the maximum for the cartridge (.253 acording to cartridges of the world).
In Australia we have lost our semi-auto and military derived rifles, but large amounts of ex military amo is still sold. I have used several thousands of rounds myself with no issues. Rounds I have used include .303 British (what else in ozzy land), .308 Winchester, 30-06, 8mm Mauser, 6.5x52 Carcano, 7.62x39 russian, and 223 Remington. Rifles range from old Muaser conversions to new comercial rifles, all bolt action.
The only points I will make is that sometimes unscrupulous dealers will sell off doubtfull amo, including one lot of 8mm that I sourced that turned out to be cleaned machinegun belt, (exciting to see tracer go out after rabits), and a batch of 30-06 that I later heard was recovered from an Argentinian ship that had sunk. Although nicely cleaned, it showed a great desire to split, hangfire, detonate with much noise and pressure signs, or fail to go off at all. When left alone for a while it developed a bad case of corrosion similar to that seen from salt water.
If it comes from a reputable source and is in reasonable shape ex mil ammo is excelent for practice on targets or on small animals (rabits make excelent practice, and rarely run off after being hit even though it is FMJ ball ammo)
Get some cheap and knock yourself out, great fun for not much more than rimfire costs.