I found Winchester white box 5.56 ammo for $9.99/20.  Is this a good price?  Also, they have blue or red box, Black Hills ammo for $29.99/50.  Is the Winchester 5.56 better ammo than the Black Hills 223?  I am still trying to learn this ammo thing??

For the extra dime a round, I'd go with the BH red - the blue is remanufactured.

If your talking about 55 gr FMJ for .50-.60 a rd,I wouldn't buy any at that price,BH red isn't worth that much IMO

Quoted: I found Winchester white box 5.56 ammo for $9.99/20.  Is this a good price?  Also, they have blue or red box, Black Hills ammo for $29.99/50.  Is the Winchester 5.56 better ammo than the Black Hills 223?  I am still trying to learn this ammo thing??

No, its not a good price. (about average)
And I don't think this is a fair comparison, either. If it is actually 5.56, you are comparing it to a .223 load. (I would rather have the 5.56)

If you have no ammo and need/want to go shoot, I would probably buy a few boxes for the range. (If you cannot get anything cheaper).

And if you have not done so yet, please read the Ammo FAQ at the top and the ammo oracle and you will know more than you ever wanted to know about 5.56/.223 ammo.

my 2 cents would be to buy some, save the cases and reload.  as long as you have good quality brass you can play with loads to get what you want much cheaper in the long run.

Define "better"

First thing (once you've read a the ammo oracle)  have you verified your rifle is chambered for the 5.56 round vs .223?
I've got nothing bad to say about Winchester Q3131 and I've always been a bigger fan of the Israeli made Q3131"A" some of my favorite 5.56 ammo.
Thing about Black Hills Blue or Red box, Black Hills has closer tolerances as far as QC is concerned. Yep it's lower pressure...loaded to .223 specs, but it's a given you'll shoot tighter groups with the BH. Black Hills ammo is known for more consistant loads than any commercial manufacturer that I know of...that's that extra $ you're paying for when you buy Black Hills. About the only way to get tighter strings is to roll your own.
Hope that helps

It is unfortunate, but amazing the universal belief, that...Buying an accurate firearm will perform with CHEAP ammo.  You have to pay to play.