Just want to join everybody in saying....22lr of course. It is the obvious choice for so many reasons, cost being top of the list. Myriad choices in ammo to suit your priorities: power, accuracy, both?, cost etc.
Who knows how long 17hmr will be available, but 22lr will survive the apocalypse together with cockroaches.
Even if you're made of money, you will see the wisdom in going with 22lr specially in your first plinking rifle.
As for the rifle, Savages in the lower price range, deliver absolutely great value for the money. Savage Accutriggers are the bomb! Ruger bolt 22s are beautiful but cost a little more and doesn't have that sweet Accutrigger.
As most 22 shooters I know have multiple rifles, you will probably eventually buy both and then some. At which point, you may want to consider any of the CZs. Having 2 CZs already, Varmint and Style, if ever I buy another CZ it will be the Scout. IMHO it is the best all around 22 to have.