I rarely get to play expert on texags but this thread is my time to shine! My dad owns a fire extinguisher business which I grew up working at and I put myself through college servicing fire equipment so I guess I am pretty much an expert in the arena!
Garage. 5lb ABC extinguisher. That is big enough to handle anything in your typical residential garage. Any fire that wont be put out by that is better handled by the fire department and is likely going to take out whatever is on fire in the garage. Don't overestimate your abilities and try to fight big fires. Plenty of folks die of smoke inhalation running into houses to try and put out fires. If you do use one, remember PASS. Pull, aim, squeeze, sweep.
Kitchen. 2.5lb extinguisher here. ABC(dry chemical) is most common but if you have the extra cash burning a hole in your wallet, call a fire extinguisher company and get a halon/halotron or clean agent extinguisher. This is purely for convenience so that when your wife sets a toaster on fire you don't have to spend weeks finding ABC powder in places all over your house. Yes, the stuff floats everywhere. The clean agent ones will set you back about $150-200 for a 2.5 lb size, plan on $50-60 to recharge if you use it. Cheap 2.5 lb dry agents probably cost $25, and are either disposable or $20 to recharge.
If you want one for your grill or fire pit or whatever go with a 2.5 gal water extinguisher. Amazon sells Amerex brand (good fire extinguishers) that you can refill yourself if you have an air compressor and they are great for wood/paper/leaves (Class A) fires. It will suck if you use a dry chem on your smoker and end up with ABC powder seasoning all over the inside. This last one is probably overkill if you have a water hose...
Inspections. Check the gauge once a year and make sure they are still in the green zone. The cheap ones from a box store are prone to leaking. If you are feeling extra ambitious, turn dry chemicals upside down and tap on the bottom 2-4 times with a rubber mallet to loosen the powder. Fire extinguishers greater than 12 years old (dry chem) or 5 years old (CO2 or water) will have to be hydrostatically tested before a company will refill them. If you buy one from a box store, make sure what you are buying has a metal head on it. As a general rule, the plastic ones are mostly disposable. A few plastic headed ones can be refiled but even some of them are labeled as "UL Classified" and not "UL Listed" which basically means they aren't refillable. If you use a dry chem extinguisher, even just a little, it will continue to leak pressure so don't squirt a little on a small fire and expect it work keep working after the initial use.
Edited to add, if you have a larger (5-20lb) fire extinguisher with a hose, take a look in the end of the hose when you do your annual inspection. Mud dauber wasps love to build their nests in the ends of the hoses. A testament to how strong their engineering is, I have seen a nest keep any pressure from leaving the hose on a extinguisher that was pressurized to 195 psi!