Ammo - start with inexpensive standard velocity ammo. This will be a 40 grain lead bullet at about 1050 fps.
I say this because I ran a test of many ammo types and given my lack of skill in shooting and wind doping, the groups were all the same size. This test included inexpensive Winchester T-22, Eley Green Tag, RWS 50, RWS 100, several Eley types,... It did not include any hyper-velocity anything or bulk pack fodder. Then you'll know it's you and not the ammo.
How To - Start at 25 yards and have some fun. Try the Rimfire Challenge (see thread on this board). Depending upon your Range's Rules, consider buying some metal rimfire targets just for fun - they're cheap, last forever and are small (transportation and storage). Work your way out to 50, 100 and 200 yards as your skills improve.
Rifle - It's really hard for me to say, I have no idea of your budget, your goals, etc.
From what I've read, the Savages are inexpensive and don't look as good as they shoot.
CZ rifles look like real rifles but seem to have hunting-oriented stocks, rather than target shooting stocks.
My favorite are older generation rifles. I have a Remington Model 37 made in their first year of production (1937). I also have an Anschutz-based target rifle.
I think if you buy a better quality rifle you will be happier in the long run because rimfire is fun, accurate and inexpensive*.
* Consider the case where you avoid shooting 5,000 practice rounds thru a centerfire rifle and don't have to rebarrel the rifle. You've probably avoided spending about $2.5k to $5k. Instead, buy a top-notch rimfire rifle ($1.5k) and shoot 5,000 rounds of match-grade ammo thru it ($1k). You will only spend $2.5k total and you still have an awesome rimfire rifle and your centerfire rifle will not need a new barrel. By the way, you'll be a better shot after 5,000 rounds of rimfire, too.