A lot of very experienced and insightful people have helped you but I thought I'd chime in too.
1. There are small bunnies that are more docile; I have owned 2 of the 'dwarf' breeds and I found that my Holland Lop is sweeter than my Netherland was. My Netherland was very sweet, too, but I only had him a few weeks before he passed so I can't be sure of how his personality would have been at maturity. Due to his small size, however, and the small size of all Netherlands, I would not suggest them for children as normal rabbits are very fragile and Netherlands (and other 1~2lb breeds) are as well. I think a Holland Lop, Mini Lop, French Lop, German Lop etc are probably something you should be looking into in terms of breeds. Since none of you have owned rabbits before, it's good to get a breed that's known to be docile and not nervous, Nethies are VERY nervous little guys! Every little thing can set them off. Similarly, you'll be learning how to hold and handle them - meaning a teeny bunny is at a bigger risk of being injured from mishandling.
I must concur that I think a rescue rabbit would be the best idea for your family - I understand how exciting having a baby rabbit is, but personalities of rabbits tend to change once they hit sexual maturity so it's hard to gauge how they'll be once they're mature. If you rescue, rabbit (usually) comes vetted, socialized, and has had desexing done meaning no hormonal behavior. They're more bombproof from the get-go. So I highly suggest rescuing should you go the route of a rabbit especially since you're new to them. The rescue should be able to guide you through owning one and help you whenever you need it, as well as make sure the bun you take home is the best fit for your family's dynamic.
2. I clean my boy's cage bi-weekly, sweep up stray poops in-between. This largely depends on housing and preference, really. Some do daily, others less frequently, but hay is messy! It gets everywhere! My boy is in my room but I'll find hay in the kitchen, the bathroom, even the room upstairs - we're on the ground floor! I'm not sure how it gets there, but hay certainly seems to get everywhere. I would also make sure no one in your family has hay allergies, they are very common and since bunnies need hay, it's a good idea to make sure no one is allergic to it as its residue will be on bunny, too.
3. Rabbits are easily litter-trained, for the most part. I've had litterbox training success with 2/3 of the rabbits I've had. First one refused any litterbox. Because of this, she had to be housed outside (She was in-tact, which is probably why she was so inconsistent but I have no rabbit vets in my area that I can trust). She was VERY messy and peed everywhere, pooped where she pleased - it was not a pretty sight. Second bunny loved his litterbox, some poops made their way out of it but he was mostly consistent. Third one is VERY consistent. Though he is in-tact and mature now, he never pees outside his box (except one time, on his donut bed... Hasn't happened since, I think he was too lazy to move LOL). The poop doesn't smell (unless gotten wet - phew!) but the urine has a strong odor, similar to cats except I notice it smells like pellets... Ammonia and pellets. It's a strange but very unpleasant smell. I only smell it when emptying the litterbox but for those brief moments, it is very stinky.
Rabbits have no "odor" on them unless they have feces or pee on them, but that shouldn't be happening anyways unless they're sick. My cat makes more smell than my bunny does.
For your husband's allergies - DEFINITELY make sure he is not allergic! I am allergic to cats and rabbits but mine is very mild, a few sneezes and that's pretty much all. But if his is more severe, rabbits may not be a good mix.
Guinea Pigs make good pets, I have heard, as do rats - they'd both be great options for a first-time pet. Rats are pretty much dogs in a teeny body. They don't live as long but they're very good pets and must be kept in pairs so you'd need two same-sex rats. I used to work in a pet shop and I loved handling the rats and the rats enjoyed being handled, too!