Generally, a lite weight/short barrel carry gun is desired to insure you will actually carry the thing. A good plinker is generally longer barreled and made of steel. These are divergent requirements. A compromise is generally unsatisfactory. If one 'type' should be bought first, I would suggest it be the one that protects your bacon.
A great example of a ccw is the S&W 442 (black) or 642 (silver). Aluminum framed, steel 1 7/8" barrel, steel cylinder, enclosed hammer (Nothing to snag on a pocket or bag/purse when presenting.), and +P .38 Special rated - and some nearly sixty years of production since it's earliest form - make it a classic. Recent and decent used examples command $300-$375 prices, while many decent sources offer it ~$450 new. Robert Mika makes a quite decent pocket holster for it - I carry one so holstered 24/7.
A great plinker can be had for $275-$400+ used. The common security guard revolver, a S&W 4" 10 or it's SS sibling, the 4" 64, can be found, often at pawn shops. At least one mail order dealer, J&G, offers a selection of such, albeit in double action only form, for <$300. You can shoot the cheapest .38 Special reloads as plinkers - and load it with decent +P defensive loads for home, camping, or car protection from 2-legged predators.
Now, if money were no object on your plinker, consider the S&W 620 or 627 Pro. These are medium-large framed 4" .357 Magnums, which will shoot mild .38s and regular .357 Magnums. The 620 loads 7 at a time, the larger 627 Pro takes 8 - in a moonclip, if desired. Both have adjustable rear sights while the 627 Pro has a no-tools changeable front sight. I would stay with the 442/642 as a CCW. I hope these suggestions help.
Stainz