When you say 'clean' are you talking about doing some basic bore cleaning (bore snake) or actually breaking it down?
Well, you decide for yourself. The mercury salts in the com-block mil surplus primers attracts moisture from the air (Mercury primers have longer shelf life, so made sense for military stocks), so basically you get a possibility of corrosion everywhere that the fumes from round going on reach, and everywhere that the salts from the primer get deposited.
If you had your bore Tennifered, or if it is chromed, you get a bit more leeway in how fast you need to clean it. If the trigger mechanisms and the action are protected from corrosion, again, you can get away with not cleaning them right away.
However, in my experience, during the hot and moist summers, you might get corrosion going as fast as in an hour it takes you to drive home from the range and unpack your gun.
There are some quick and dirty remedies to neutralize the mercury salts, with the most common ones being using original Windex (the one that has ammonia) to swab the barrel at the range (ammonia neutralizes mercury salts), or firing 10 or so (number people quote seems to differ between 5 and 20) rounds of commercial non-corrosive 7.62x39 ammo at the very end of your shooting session, since subsequent shots will "burn away" the salts deposited by the corrosive ammo.
Oh, and yeah, definitely suggest CZ858 non-restricted as a "fun" gun to get. Relatively cheap for a modernish semi-automatic, full parts kit (sans stock, action and barrel) costs 99$ from Wolverine, and you can dress it up in plastic and resin or into wood to your hearts content. The only downside of CZ858, is lack of a decent place to mount optics (read site mount is a fair distance forward), but, truth to be told 7.62x39 is not really a sniper round, so iron sites are usually good enough.