Here's my two cents. Your present situation can work for you by following some simple procedures. Many members have no choice but to buy lumber at the box stores. Either they don't have the milling machines, or some may not even have a table saw. The point is, if you understand what you get at the box stores, you may be able to deal with it.
For a good glue up, jointing and planing would be ideal, but with box store lumber, you are committed to use the edges as they are, unless you can create a nice straight flat 90° edge that's suitable to be mated to another one done the same way. There are other ways to get that edge, like with handplanes, but getting proficient with them takes some practice.
So, we are back to the edges as they are. Keep in mind that those edges may not be sharp and clean. The corners (lengthwise) may have damages, divots, or could be slightly rounded. So, clamping them together will not give a very tight looking seam. That's what doing the edge work will take care of. In lieu of a handplane, you could mate up the edges across the top, and see where a board may have a high spot, and use a block of wood on the edge to sand it a little at a time and see if it makes for a closer fit.
As for clamps, if the edges are flat and straight, they should mate up with minimal clamping pressure. When I started out, I used mostly pipe clamps. I would find the clamp ends at flea markets for $5 or less each. Garage sales could have them for $5 - $10 with the pipe. So, if you are under a finish schedule, you may not have the time to go shopping around. I would try to make do with what you have.
About your glue up. You should first do a dry fit to see how the mating edges look. If they were jointed and fit without any gaps, you can proceed to the glue up.
Have all your parts, glue and clamps all ready, and laid out. You don't want to be hunting for something at the last minute. It seems at this point it's a simple matter of applying glue and just setting the clamps and cauls and tightening them up.
Clamps, like pipe clamps for instance have a closing pressure from the clamp ends that can exert more pressure on an upper or lower edge of the board other than the center, if not positioned properly. Many of those clamps the ends do not close under pressure absolutely parallel to each other.
When tightening one of those its a good idea to see how the mating edges are reacting as the clamp gets tight. Alternating the clamps position on top of the boards and the bottom of the boards help in creating a straight line of pressure to bring the boards together.
As an example of an improper clamp attachment, lets assume that there is slightly more pressure along the top portion of the edges versus the bottom. As the clamps tighten, the pull can make the combination of boards bow, or curve into a "U" shape. This would be indicative of all the board edges (that may be flat to each other) and the faces take a shape other than horizontal. The other side...meanwhile...will show that the glued edges are not tight but slightly separated allowing the board to tip away from its mating board. Over clamping (too much pressure) can do this.
The whole point to this drawn out description is when setting clamps to the outer edges of a group of boards, insure that they are set to exert centered pressure to the boards.