1) On average an accident occurs once every 18 years of driving, regardless of fault. Based solely on that statistic it makes more sense to only carry liability insurance.
2) I would get a car around the same year, with less mileage. If you go by insurance company methods, if the damage is >75% the value of the car, you are better off junking it and getting a replacement. Personally I wouldn't purchase a car with more than around 130k miles, or older than 15 years, but that comes down to preference. I expect 5-10 years of use out of every car I buy
3) Honda civic, fit, accord if you need the space. Toyota corolla, matrix, yaris, prius. Mazda 3/hatch. Read the edmunds consumer reviews for the year and model of a car you are interested in once you locate one. If possible, try to find a vehicle with no reported accidents.
4) If you can, have an independent mechanic inspect the vehicle before you purchase it. Do some research, inspect the tires and wheels, the brakes, check the date on the battery, and inspect under the hood for leaks after test driving. A carfax report helps immensely with knowing what maintenance was done, but if the car was serviced by an independent shop, chances are the carfax will not tell you much.
My $.02, hope this helps.