Get a Jeep Cherokee, if it's not been abused with off-roading those things will last and last and last. Our 1993 jeep we had to get rid of because after 20 years at the beach the body finally started rusting out to the point it was raining inside the car, but the frame and engine, and transmission were still in excellent condition. Our 1998 Grand Jeep Cherokee is still going strong, even though we've had it for... 5 years or so.

Most vehicles built for off-roading will last for-freaking-evar on normal every day street driving, you'll have a decent amount of cargo space for groceries and even passengers., though oyu might be paying a little more in gas.

For regular use: we had a dodge minivan that lasted for over 16 years

Why didn't you send me a message over skype dear? You know I can help you pick out a car!

So,

There are a few questions to ask.
1. Why has your car broken down?
2. What other potential issues are there that your car could develop?
Aka, is it worth looking into repairing your car?

This is something you need to consider - getting a new car itself can be rather expensive.
That is the next layer of questions;
1. What is your budget range?
2. What year car are you looking for (May be largely determined by #1)
Used cars can generally range between $4,000 to $14,000 even for the lower costing ones, depending on the year. Of course, this largely will be reflected by the make and reliability of the car as well. GM Cars probably aren't going to be worth as much due to all the recalls (Chevrolet, Buick, GMC, Pontiac, Saturns, etc). Then there's all the cars affected by the Takata Recall. Granted, even before everything that happened, I would never get a Volkswagen.

Once you find a car add that looks good to you: Look at the VIN # and go to the manufacturer's website and check for recalls. You can do this at the dealership or private owner as well if you have a smart phone.

It also depends on what area of the country you are in (IE, up around Detroit, it might still be a bit difficult to find a good used car due to the flooding that happened a little over a year ago).
Remember that Carfax is easy to manipulate - I've had dealerships actually refuse to report data on accidents involving vehicles they leased and had to get the data from other sources, such as Autocheck: http://www.autocheck.com/vehiclehistory/?siteID=0

Also, always do a visual inspection of the car.
Look at the doors. If one has a gap larger than the others when open or otherwise appears to be out of alignment, that is a good indication the car was in some kind of an accident.
Look at the exterior lights - anything that was marked with an X was either replaced or lined up for replacement.
Look at the underside. Find the brake lines, see how rusted they are. There will be small, metal tubes along the car either along the passenger or driver side, depending on who makes the vehicle. They will be maybe a quarter of an inch large. Find them, make sure they are in good shape.
Look at the fluid levels. If the fluid is black, it's bad. IF it is grimy, it's bad. The owner should be replacing this before they sell you the vehicle - especially a dealership. If it's transmission fluid and it's sludgy, get another car.
And ask about repairs and what the vehicle has been through.
Look at the check engine light - both before and after you drive it around. Some places have emissions checks that require this to be off. But if it is on, that is a sign that there is some kind of maintenance issue. Not always - electronics can malfunction too, but you're not looking into a car to buy it on the basis of what issues it may or may not have. It's better to know what issues there are and to have a plan on how you are going to deal with them...
Look at the tires - do the quarter test.
Oh yes, ask if they still have the owner's manual. If they don't, then ask them how they maintained the car. Most owners manuals you can find online. But if they can't answer that, there is good reason to question the car's maintenance.

Remember, if you are popping the hood and getting on the ground to look at a car, you're doing what no one does already. Dealerships will know you're serious about your purchase and won't be as likely to try to lie to you. Especially when you've gone to other dealerships already and have been doing the same thing. After doing this to about a few dozen cars, they'll get the picture.
Many people are also not knowledgeable about cars. When you start to do these basic things, you'll become more knowledgeable and will have the upper hand on picking what you want.

The next step is to start picking out what types of cars you have the budget for and want to look at.
Kbb.com is a great place to start.