Should I care about brands of tires? My MTB is due for a tire replacement. I'm also trying to get into long distance biking. Budget is a big concern right now but also I don't want to have to replace my tires so soon.

Is it worth getting the cheapest tire? Not really doing cutting edge stuff so proprietary lug design or w/e don't apply I think. I do want some slicks.
Very cheap tires are likely to have little or no puncture protection. Unless you're riding under very optimal conditions, slightly higher quality tires are worth it when you consider the time/cost of replacing or patching punctured inner tubes.