Drill press sizes are called out by the center of the circle that they can drill, or, putting it another way, twice the distance from the center of the chuck to the column. Yours looks to be an 8" or 10" press. Not big, but I had a similarly sized Delta drill press for years as my only drill press, and it was quite handy.
The big virtue of drill presses for hole drilling is that they'll drill a hole at an accurate right angle. For the dollars, if your uses are only now-and-again, you did well.
That looks to have a tilting table. One issue with cheap drill presses can be a table that's not at a true right angle to the chuck, which will mean your holes aren't, in fact, accurate after all. To test this, raise the table to examine the angle setting; there's usually a pivot bolt, and a pin to hold it at the neutral (not tilted) position. Make sure that's all in place, and unplug the drill press. Take a piece of stiff wire* and bend it into a sort of "Z" shape: a right angle bend long enough to fit into the chuck, a center section as long as half the edge-to-edge measurement of the table (if the table's not square, use the measurement from the shorter side), and another right angle bend down. When you finish, and the wire is inserted in the chuck, you'll have something that will sweep around the edges of the table, with a finger pointing down. Move the table up until the finger is just barely touching the table. If this is too hard, get it close enough to insert something like a feeler gauge between finger and table. Now, rotate the chuck and test your measurement at various positions around the table. If the measurement comes out identical or darned close to identical, that's OK.
Test runout by chucking a drill bit that you know to be straight (usually a large diameter drill bit will be more likely straight than a small one). If you happen to have a smooth piece of rod of known straightness, that's even better. The drill press is still unplugged, right? Good. If you've got a dial indicator, set it up and rotate the chuck by hand, with the indicator against the smooth portion of the bit, as low as you can get on the bit without hitting the flutes. If you don't have a dial indicator, sort out a way to clamp a smooth piece of steel or hardwood close to the bit, and use your feeler gauge to check clearance as you rotate the chuck. This is less reliable, partly because there's a fine art to using feeler gauges. They're called "feeler" gauges because you have to develop the sensitivity to tell when the fit is the same on a particular thickness from one setting to the next. A couple of thousandths of runout: worry not. Huge runout: bad chuck, badly installed chuck, bad bearings, or generally poor machining of the parts.
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*If you've got a wire coat hanger, that's about right. Or the wire used for political lawn signs, which is probably easy to find right now.
