As others have suggested, you can use a circular saw and a straight edge and get decent results! Although, I like the shooting board as when you lay the jig on your piece of wood, you know exactly where your cut is going to be made.
I found a video of such a jig on the internet.
Basically the jig is just one piece of wood screwed on top of another. The top piece serves as the edge guide for the saw, so the edge of the top piece must be perfectly straight! After securing the two pieces, the saw is then used to trim off the excess on the bottom board. You now have a jig that will provide accurate cuts. But I should add, it will only work with YOUR circular saw and the blade that you use to cut the jig.
This is difficult to explain (although the jig is very simple), so I would suggest watch the video, then come back and read my post.
To keep costs down, and if you are dead set on hiding all your screw holes, I might also suggest another method of joinery. You can buy a set of bits to use with your drill that will serve as countersinks and plug cutters. So, when you drill your screw holes, countersink them. Then cut plugs out of a scrap piece of wood, and use the plugs (and glue) to fill your countersunk holes. Once the plugs are sanded, it is very hard to see them. Or, for a different look, you can cut your plugs out of a wood that is very different from the wood you are using for the main part of the assembly.
Other suggestions you have received are very good.