You are starting off with a fine rifle. I have one just like it myself.
Your expectations are a bit off however.
You need to figure on spending at least double your 400.00 figure for quality glass. If you get lucky you might be able to pick up a used Leupold 3.5-10x50mm for that price if you are patient and watch the classifieds here at LRH and good ole Ebay, but that is just barely enough to get you started.
You would be better advised to save up your money for a few extra months so you can move up to the same scope in 4.5-14 or the Vortex Viper PST in 4-16x50, or perhaps the zeiss conquest 4.5-14x50.
If you don't start off with quality optics you are going to end up frustrated and spending a good bit more money. The only alternative I can recommend is a high quality fixed 10x or higher power but then if you end up needing to make a shot at close range you will have too much.
The best advice again is to be patient, save your money, and get the best possible glass you can afford.
Now that we have that covered.... .
Go ahead and isntall pillars, float the barrel, and bed the action well. A competent gunsmith can do the above for you for 200-300.00 or you can do it yourself if you are a handy kind of guy and willing to sit through "how to" videos on Youtube.
Next I'd work on lapping the bolt lugs, trigger group and get the trigger adjusted to where you have a clean, crisp, light trigger that you are comfortable with.
Once you decide on your scope, I'd recommend EGW HD zero MOA rail, and TPS scope rings. Great equipment that won't break the bank.
As for see through rings, I've never seen a set of them that were not crap so I'd say avoid them.
