If you're concerned about steeper or longer hills, 3-speed is not the best option. They tend not to have very low "hill gears." But other than that, they are great. Occasionally, If find myself missing some between gears, but the only one I really miss is the hill gear. The first gear on my two 3 speed bikes is low enough to climb hills if I stand up and pump. As I get stronger, that is less often.
Yes, internal geared hubs (IGH's) are less maintenance and more durable than external derailleur type gear systems. There's no doubt about it. I also like that most IGH bikes have an option for a chain guard, but they're also more expensive, so you have to decide how much that maintenance time is worth to you. For example, a Trek Allant commuter with 21 speed derailleur costs less than a Trek Belleville, with 3-spd IGH.
I think it's nice to have some of each. Bikes are cheap enough we can have more than one. It's just a matter of deciding which one to get first. In that case, I recommend the multi-speed derailleur bike first, as they are just more versatile and offer more for the money. You will never wish you had more gears, and you can cope with the extra maintenance easily enough in the meantime.