Do I check the price at close on Friday and then set up a stop limit order at a quarter of that price? I am trying to figure out how to be ready for when the market opens on Monday morning to get in on purchasing two shares.
If you only have $450 to invest, you can't purchase a full lot of 100 shares even after the split, so you're going to find a broker that will trade "odd lots". If that's the case then it doesn't matter if you buy before or after the split.
Say AAPL is trading for $500 at the close on "split day". You could (if your broker supports it) buy 0.9 shares at that time.
The next morning, AAPL will be worth (all else being equal) $125 a share, so you could buy 3.6 shares. Or if you bought the night before, you'll have 3.6 shares worth $125 each.
You're in the exact same position either way. There's no "magic profit" with splits, so if you're buying fractional shares anyway it doesn't matter when you buy.
As a side note, any order you place today will probably be adjusted after the split. So even if you set a limit buy for 1/4 of the price, it should still be for 1/4 of the post-split price.