There are always terms and definitions that need to be clearly defined...particularly "accuracy." What type of accuracy are you looking for? If you are looking for sub-moa 100 yard groups, than no a 10/22 may not be what you are looking for...especially if you don't have the money to put out. I'm sorry, but you are not going to build a decent "target" rifle for less than $500.00. Here is my story and experience...
I went on a quest this past summer to build a sharp shooting rim fire rifle and ended up being talked into a Savage 93R17 FV. I have fallen in love with it, but it did not fully satisfy what I wanted. I wanted to be able to go shoot and not break the bank. As i said, I love the 17, but 50 rounds at $14.99 vs 22LR 500 at $19.99, no comparison. To the credit of my 17, it is one mean machine that I absolutely LOVE to shoot. My purchase included the Savage 93R17 FV, BSA Sweet 17 6-18X40 Scope, Red Head Base and rings, bi-pod, 250 rounds and a bore snake for a total of $600.00.
After a day at the range I realized that although I love the rifle, it was a lot more to shoot than what I originally wanted. I decided a few weeks ago to build another rim fire, this time sticking to the 22LR. I got lucky to find a 10/22 someone had built and decided he wanted a bolt so was unloading it cheap (he works for one of the local gun shops and gets good prices to start with). he just so happens to be a Marine as well and made me a steal of a deal on the rifle. It has a Green Mountain blued threaded bull barrel and custom stock with BSA Sweet 22, Warne base and rings...cost $400. Needless to say, my quest to build a 22LR came to a screaching halt because I could not build it better or cheaper!
Result, I love both rifles! Either way a squirrel is dead! If I'm wanting to impress someone punching paper, the 17 is going to be tighter. If I want to have fun and shoot a lot of targets with great results, 10/22.
Think very hard what you want to do with it. I was lucky to have some funds to build or by a second rifle because even though I love the 17, I would have not been happy for what I wanted to do. IMO, you can't go wrong either way. If you buy the package deal (Savage), you can't go wrong!