The only choice of tech that would actually affect anything is the last zerg research. Basically, if you have disruptor, take out the air, if you have emulator, take out the worms. This doesn't mean, however, that if you do the opposite, it's game over. I've managed to beat air with no emulator and ground is easy even without the disruptor, hordes of siege tanks behind bunkers at correct choke points don't leave any chance to zerg, even if you slack some on the worms killing. If you play against air with no emulator, it's a bit harder, but still fully upgraded vikings are ridiculously OP with crazy range and AoE attack, and you don't need as many siege tanks as you need against ground. There are various tactics on how to deal with Kerrigan, starting with mass sniping with ghost and ending with stunnign with thors, none of those actually require any of the techs. Or the ridiculously easy spamming her with mind controlled broodlords, if you have the emulator, her silly AI would keep hitting broodlings, while you blast her away safely.
The rest of your research barely affects anything, even on brutal, the only mission I would call hard on brutal would be In Utter Darkness and it's not even terran. Yeah, sure, it's nice to have tech vessels for Engines of Destruction, but you can just mass cloaked wraith and wipe the last bases even before Odin gets there. Some researches would give you some luxury, like mining gas with no SCVs, so you can have more actual army, or instant supply depots, which would make sure you're never supply blocked, but once again, it's all luxury, and you can easily live without them.
Edited by Deniska on 4/21/2013 8:27 AM PDT