Welcome. I'm aboard the 'buy the .22 first' boat, pushing a different name at you; Remington 597. If you're not interested in modifying it it's my opinion the 597 offers a little bit more for your dollar. The 10/22 is FAR more supported in the aftermarket. I however like to just shoot them, and nearly 3 years later the 597 has never disappointed me. 1" at 25 yards with a good scope is all-day-long easy, bone stock and never been apart.
Pistols, I'd say buy what your heart wants and shoot it when you can. I bought a 9mm, and even it's far-less-than-.45 cost to shoot it still stings to go through $100 an hour having fun. While I don't at all regret my purchase (Jericho 941, based on the CZ75), a .22 pistol is in my future.