You say 22 lbs, but are you wanting something that has a 5 point harness and can rear face? That is safest. Also safer to keep your child in a carseat with a harness as long as possible. A lot of the seats now you can keep them harnessed alot longer. It is hard though to find a GOOD seat that rear faces, works as a front facing convertible and can convert to a booster. It is just hard for them to do all of those jobs well. I would suggest getting a convertible that can rearface and has a high harness weight limit/height limit. Then you can buy a booster when the old seat is outgrown. There are alot of good bosters out there for around $50 or some even less so it's not like you are going to be spending a lot when that time comes....and it is years down the road.
Britax is great, whichever model, if you can find one for under 200. Graco makes a MyRide 65, which converts, rearfaces and harnesses up to 65 lbs. Also the First Years Truefit or Evenflo Symphony 65, or Sunshine Kids Radian 65 or 80 (those are going to be on the pricer end too).
If your child is over 2 you can buy some that front face only and convert to a booster and do good job of doing those two jobs. Graco Nautilus is a great affordable seat in this category. But like I said, injury risk is much much higher if you turn a child front facing between 1-2 and you should keep them rearfacing to the rear facing weight limit of the seat. Britax makes one like this too (Frontier) but I doubt you will find one for less than 200.
Diaper bag my all time fav is my Land's End backpack diaper bag, but sadly they don't make them anymore. I would just buy a nice quality back pack with different sections. I've heard Skip Hop is nice too. But most of the more "stylish" ones either aren't very functional or just don't work very well.
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Just a note on your comment, you don't want a forward facing seat after your child grows out of an infant seat. You want an convertible seat (like I mentioned above). They are called convertible because they convert from a rear facing seat for the younger child to a forward facing seat after they outgrow the rear facing weight limit. So when they reach that limit you turn them forward facing in the same seat. Then when they outgrow that seat, then you buy a booster. Unless you have a very high weight/height limit infant seat (and some do go up to like 32 lbs these days so check your manual) you will want to continue to rearface the child until they hit the rearface limit of whatever convertible you buy (hopefully this is not before the age of 2). I had standard infant seats that my boys grew out of usu by height before weight, but their max was 22 lbs. They both grew out of theirs between 4-6 months. The absolute minimum (but NOT the safest) age to front face is 12 months. So no matter what if you have a seat that the weight limit is 22 lbs, you are going to need to rear face, unless your child is just very very small, and in that case it would be important to keep them rearfacing anyway since they could be thrown around more easily. Please look into the rear facing issue though, the AAP recommends keeping them rearfacing as long as possible now.