No matter what kind of saw you end up getting, make sure you get a decent quality set of blades for it and a fence that locks in place accurately.
It may also be worth your while to check local listings for used tools ... you may be able to afford more than one, in this way, but you may have to do a little extra work to fit them in your shop and properly outfit them with the accessories you will want to use and the things that they need.
For any saw, a fence for the work to ride against is generally a must .... if it's adjustable, it needs to be accurate from both sides of the saw blade, to prevent binding and burning of the wood.
If you are not using a fence, then you should be using the miter slot(s). You can create a jig that your work can ride on/in that secures it in position for certain repeatable cuts. These jigs are referred to by several different names, one of the most common being a "sled". These are made to have (usually) 2 runners that fit into the miter slots with no wiggle room or play, and will run the length of the table without binding. They have a base board that connects the left runner to the right runner (or rides against the fence, if there's only 1 runner), that carries the work piece, and a backstop that the work piece is clamped to. There may be adjustable or permanent stop blocks in place, depending on the type of work being demanded of the jig.
These jigs can be used for table saws and band saws alike, though with a table saw the backstop is tall enough that you simply run the entire thing over the blade with each pass, and with the band saw, you do NOT run the backstop through the blade, instead stopping the cut and backing straight out.
With any type of saw, you will want to tune the blade as well ... for a table saw, the blade head must be perfectly perpendicular to your miter slots.
With a band saw, you want the leading edge of the blade to be right on the crown of the wheels, so that it has the least possible deflection, and will therefore tend to cut a straighter line without veering to one side or the other.
With a miter saw, you want the blade set up to be perfectly perpendicular to the fence.
The last thing I would like to mention is .... ease of fabrication.
It would be very difficult and time-consuming to CREATE a bandsaw. I've seen plans for one made out of wood .... someday, I would love to build that thing and call it my own. For now, though, buying one would be the better idea.
On the other hand .... I can easily see how taking a circular saw and converting an existing table top or bench top into a table saw is more than doable ... I simply have to mount the saw accurately under the table to be perfectly lined up so that my clamping fence will be perpendicular to it ... cut a few miter slots into the surface, and it should be good to go. I may not have the depth of cut right away that I would like, but after it's set up I can grab a router and cut the slot for a surface plate and cut out where the saw will sit under the table and she'll be ready to rock.
I already bought the circular saw .... it was 35 dollars at harbor freight tools. If I leave off the table legs and just use the top, I can just take it down and stand it up by the wall in the corner out of the way ... or better yet, just take some strong hinges and MOUNT THE TABLE TO THE WALL with fold-out drop down legs on the front, and just fold it up out of the way when it's not in use. I can mount my router on the same table if I want.