Should I get a single- or two-stage furnace for my three-floor brick home?
2 stage is always the way to go but as with any furnace must be sized right. To size a furnace properly a contractor should use ACCA Manual J or equivalent. The furnace should be sized based on the coldest anticipated temperature(minus the worst 3%). Since it is not that cold very often your furnace is almost always too large for your house. A two stage furnace helps to alleviate this by using the low stage when it is not too cold. If your furnace is too large there can be large temperature swings. The proper size furnace keeps temperature more even. Some contractors try and use two stage furnaces to makeup for them not doing a proper heat load calculation usually ending up with a furnace that is too large. If sized correctly and operated with a good 2 stage thermostat that actually calculates how fast the temperature is rising, two stage furnaces are awesome. 
Variable speed furnaces are very reliable and their motors are much more robust than normal motors. I have seen their “brains” scrambled on a few units without surge protection. I generally only remommend variable speed furnaces if there is air conditioning involved. Variable speed is great for controlling humidity during cooling and they take less electricity so your savings adds up quickly if using for air conditioning too. 
Two stage furnaces are only $300-$400 more than single stage and variable speed furnaces about $500 more than that. You will need to add for a good 2 stage thermostat and possibly running an extra wire.