I'm hoping your order was mixed up and you're going to do the engine swap before you change out the header (remember, you only have one.)
Your cheapest route to hp gains will always be a (homemade) turbo, but you could end up sacrificing reliability in the long run if you choose to go that way. An engine swap is a good way to (significantly) increase hp without sacrificing reliability. Just make sure to shop around for a good price.
As far as the header goes, that's a start. You'll also want to replace the exhaust (catback). Think of your car like a hose. Your engine is the spigot. Your header is the half connected to the spigot, your exhaust is the half where the water comes out. What would happen if you increased the diameter of the hose connected to the spigot but not the other half? Well, you'd have better flow initially, but it would end up bottlenecking once it hit the non-upgraded section of the hose and eventually the whole thing would get backed up anyway, pretty much just the same as if you had never upgraded the hose to begin with. Now if you ALSO increase the diameter of the open end of the hose, the water will flow through the entire house completely unobstructed.
If you increase the diameter of the header pipes, the flow can ultimately become bottlenecked when it hits the exhaust. Upgrade your exhaust as well, and you'll have that free flow.
Aside from that, pick up an ebay intake (don't waste your money on AEM or other expensive name brands). This is one of only a very few areas you are allowed to cheap out on. Buy an ebay intake and a K&N filter and you'll be good to go.
Welcome to Club Civic!