I usually start off with a Harbor Freight, or similar, economy tool. The experience will teach me whether the tool is worth having on the truck, and what features I desire when I get a "real" one.
I have found the HF rotohammer, demolition hammer, and jackhammer to be perfectly satisfactory. The bandsaw. "multimaster" clone, and bench grinder are also fine. The angle grinder is prone to having switch issues, but is useful.
The HF 'saws-it-all' is a major PITA and poor performer. Their 'hole hog' is also prone to having something inside break. Economy saber saws (mine was a B&D version) work- barely.
Cordless tools? Cheap ones have poor batteries and are prone to charging problems. Don't waste your money, not even once.
I haven't used any drill, let alone a corded one, in ages. For me, the cordless impact driver is king- and it's amazing how much work I can get out of my little 10v, pocket-size Bosch. There are plenty of drill bits out there with the hex shank you want. I even use mine to drill wood framing with auger bits and metal with my Unibit.
Regarding corded hammer drills ..... there's a tremendous difference between brands, even corded brands. For holes under 1/4", my cordless one does just fine. For anything larger, you probably want to skip the hammer-drill and move up to a roto-hammer.
It's telling that my $75 roto-hammer has at least $400 worth of bits with it. Don't leave the price of the accessories out of your tool budget. Even my saws-it-all has a couple hundred $$$ in blades and accessories. (Visit Paws-Off tools for some nifty accessories for your saw).
Which brings up one problem with the cheap tools: poor, or non-existant cases. Fortunately, I am able to use ammo cans for most tools. The roto-hammer, hole-hog, and saws-it-all each fit nicely in the smaller 40mm ammo can.