Find a deflection calculator online and start putting some numbers in. You will be amazed at the difference certain changes make.
If I was to start from scratch I would use large square extrusion for my uprights rather than plate. Unless you find cheap scrap plate, it'll often be cheaper to buy a length of extrusion than the large plate need for gantry sides. Have a look at the moment of inertia for various extrusions.
See cnc router parts or kronos designs for examples. I think the most frequent weak point in most diy designs is the gantry uprights, usually plate with minimal bracing. These can easily bend or if using round rail allow pivoting.
7xCNC.com - CNC info for the minilathe (7x10, 7x12, 7x14, 7x16)