Note that I really enjoy building wheels so I'm a bit biased here, but...as long as you inspect them when you get them, machine built wheels are usually okay.
The (main) differences between machine and hand:
- Quality of components. Generally machine built wheels use cheaper components.
- Logo in the right place (you should see it centered under the valve hole) - purely cosmetic.
- Tension brought up slowly and evenly on hand built wheels. This (and hubs) would be my main concern. The machine will make sure everything is true, round, and dished...sometimes better than a person can do...but it may not get there smoothly.
With (1) my concern would be the quality of the rim, mainly the braking surface and the weld, and the quality of the hub. The hub quality, especially at low speeds, is going to have the most impact on how "fast" a wheel is. Weight (spokes/rim mostly) will have some effect on climbing, but not much and with the big tires you are going to roll, I wouldn't have much concern here.
My concern with (3) is primarily how well the wheel will hold true and round. Most folk will occasionally check trueness of the wheel, but ignore roundness. You can check both without a truing stand, but to check roundness you need to take off the rubber. If you're willing to check a couple of times after you've put some good miles on them you should be fine.
My $0.02 is to look for wheels that have decent rims and good hubs and then give them care, especially during the first 1,000 miles or so. On a budget, I'd rather see you pick up some machine built wheels with good hubs then some hand built wheels with bad hubs.