Quoted:
I always thought the straw purchase law was about if you are specifically purchasing for a person who you know can't pass the background check themselves.  I know I've bought multiple guns for people as gifts and never had a second thought about it.

Quoted:
If someone gives me money to purchase a gun for them, that is illegal.

Yes, even if they're a relative that could legally buy the gun for themself (a recent Supreme Court decision).

If I purchase a gun with the intent of giving it as a gift (to a parent, sibling, grown child, etc) would that be illegal?

No, as long as they can legally own the gun.

If I take same said person to the store, let them fill out the paperwork, but I pay for it, is that allowed?

Should be fine legally, but the shop might balk at the sale as it could give the appearance of a straw purchase.  The ATF actually recommends giving a gift card to allow the other person to buy the gun in their name.

Question 11.a. Actual Transferee/Buyer:For purposes of this form, you are the actual transferee/buyer if you are purchasing the firearm for yourself or otherwise acquiring the firearm for yourself (e.g., redeeming the firearm from pawn/retrieving it from consignment, firearm raffle winner). You are also the actual transferee/buyer if you are legitimately purchasing the firearm as a gift for a third party.ACTUAL TRANSFEREE/BUYER EXAMPLES:  Mr.Smith asks Mr. Jones to purchase a firearm for Mr.Smith. Mr. Smith gives Mr.Jones the money for the firearm. Mr.Jones is NOT THE ACTUAL TRANSFEREE/BUYER of the firearm and must answer “NO” to question 11.a. The licensee may not transfer the firearm to Mr. Jones. However, if Mr. Brown goes to buy a firearm with his own money to give to Mr. Black as a present, Mr. Brown is the actual transferee/buyer of the firearm and should answer “YES” to question 11.a. However,you may not transfer a firearm to any person you know or have reasonable cause to believe is prohibited under 18U.S.C.§922(g), (n), or (x).

Quoted:
Ok, but if Mr Brown buys the gun and then gives the gun as a present to Mr Black (who is also legally able to purchase a firearm), there is no paperwork showing the transfer from Mr Brown to Mr Black. How much trouble could the government possibly cause because of that? Questions that come to mind- Well if you could legally buy the firearm, Why did someone else buy it for you? Why didn't he give you the money so you could buy it yourself? I just don't see a win situation if somehow the government gets involved in such a transaction. If there becomes some kind of gun registry, and I'm supposed to have an ABC gun but I traded it to Mr Smith for a shotgun, then that will bring in a whole different investigation as to why we have each other's guns, what else have we traded around, who else is involved, is there a conspiracy of some sort, etc.
Back to the reason of my question- I gave my son(of age and legal to buy himself) the rifle his mother bought me for Christmas before he was born, and the shotgun my dad gave me for graduation. Both guns purchased before all the background check stuff. So the paperwork is not there. But I was thinking about buying him a new revolver for Christmas but I don't want anything to look suspicious from any angle. So I am trying to decide to either buy the gun myself and then give it to him, or give him the money and let him go through the application just so its in his name.