To paraphrase Forrest Gump, "buying a 10/22 is like opening a box of chocolates, you never know what you're going to get." I've found some to be plenty accurate out of the box, others needed work. Some lots of work.
I wouldn't start with the basic standard carbine unless I just had one and was prepared to replace the stock, barrel and trigger. Which with the 10/22 is easy enough for a home DIY project. Ruger offers around 80 different versions of the 10/22 if you check out their website. I'd start with one of the Sporter models to get a better stock and have better odds of a more accurate rifle out of the box.
Ruger® 10/22® Autoloading Rifle
The factory trigger can be worked on, and the factory BX trigger is a big improvement. Either way, whichever is easier for you and less expensive.
There are lots of options for aftermarket barrels. They don't have to be a heavy barrel to be accurate. I put one of these on one of my rifles and accuracy improved dramatically while maintaining the factory barrel contour.
E. R. Shaw Barrel Ruger 10/22 22 Long Rifle Sporter Contour 1 16 Twist (midwayusa.com)
Of course a heavier barrel will help steady the rifle and it isn't hard to keep weight to around 7 1/2 lbs even with a heavier barrel. That is about the same as a factory centerfire big game hunting rifle.
There are lots of options ranging from about $100 to over $300. Of course with a heavier barrel you'll have to either modify the factory stock or buy a new one.
ruger 10/22 barrels - MidwayUSA