Simply, if you need to stop the car in a hurry while it is raining, snowing or icy, without rear brakes the front wheels will lock up and you will lose control of steering as long as you have your foot on the brake. The car will slide into whatever you are braking to avoid, without really slowing down much.
The rear brakes don't do a lot of the stopping, but they are necessary to prevent weight transfer to the front of the car during hard braking. Think of them as an anchor for the rear-end of your car while you are braking. Even if you have ABS, the car is still dangerous on slick roads because ABS increases stopping distance while they are active as compared to hard braking on dry pavement, although they do allow the driver to retain some control of steering.
You can get away with it for a few weeks, since it's summer, but I would be very careful driving when it's raining. Especially in neighborhoods. Do less than the limit, pay attention and don't tailgate anyone.
The rear brakes, assuming you have disc brakes, can be very inexpensive to get up to speed. Disc brake pads are cheap and very easy to replace. But often they are not cheap to replace at a garage. Many garages take the angle that the rotors need to be replaced because they cannot legally be cut or turned (same thing), because the factory rotors were too thin. Also, garages will tell you that you need new calipers. This is how two brakes become a $1000 - $1500 job. It is almost never necessary to resurface rear rotors, as they don't often warp, and even if they are scored they will do the job with a new set of brake pads. And calipers do go bad, but not often.
The muffler should run you under $200 installed. As far as the rear suspension goes, shocks are inexpensive and easy to replace. I would guess you have rear shocks. I think if you are not completely relying on a garage to do this work, and are at all mechanically inclined, you can do at least the rear brakes yourself. If you have rear shocks (not struts, you don't want any part of doing them), you can certainly do that yourself as well. The muffler might be more trouble than it's worth. The more you can do yourself the better.