You can train a Cat it's just harder and takes more patience, Cat's make you work as hard as they do but they are great companions and very in-tuned with your emotions. Our Cat knows when one of us is down, depressed or upset and lets us known she knows.
Depends a lot on space and the amount of love and attention you want to spend. Remember a dog = a lot of attention.
Also if you decide on a pet can you please look at animal shelters too... there are a lot of doggies and kitties that needs homes. We have a Pit mix (from our local SPCA). He is a medium sized dog but very strong. He plays a lot but he sleeps a lot too. He also get this "manic' thing were he just runs and runs.
We also had a kitty but that was way back. My brother is seriously allergic to kitties.
Maybe test everybody in the family for dog / cat allergies too. Would be a shame to get a pet that makes somebody sick.
We have always had birds too. Bugdies can be trained to talk just like African Greys. Budgies are a bit cheaper and easier but they live about 5-10 years. Cockatiels are a bit bigger and live about 10- 15 years, they are also easier to maintain. Birds like Grey's, Cockatoos are a major investment and have a lifespan of up to 60 -80 years. But they are a smart as small children. My nephew has a Grey. It, for instance, asked on a Friday for its sweet (it 's allowed one a week). So on a Friday morning when he gets up for work it askes him "ek wil my smartie he" "i want my sweet". So it knows when it's Friday.
Hope that helps a bit. Sorry for the wall of text.