I train as a boxer and it is very good for fitness and stress relief. I havn't used free standing punching bags as we have hanging ones but I'll try to help you.
I would assume that the free standing ones would be designed to not topple over, otherwise they wouldn't be very popular...
A few things to note:
If you just punch the bag with your bare hands you can do serious damage to your wrists as they can bend easily. You should wrap your hands in bandages and use proper gloves. You can buy specially made bandages from boxing shops or just use some from a drug store. I wouldn't recommend using 'bag gloves' that you can buy for $20, these are $#iT and don't protect your wrists.
You should also learn how to punch. If you punch the bag wrong you could do serious damage to your wrists and hands. My coach (60 years boxing experience) says that you should connect with your 3 outside knuckles, ie. not the index finger knuckle. And you should try to punch straight and through the bag, not the bag itself.
My wrists were very sore for the first few weeks as I had not done a lot of punching. Now after a few months all of my joints (fists, wrists, elbows, shoulders) feel the strongest and healthiest they ever have.
A typical bag routine (to simulate an amature fight, 2min rounds, 30 seconds rest):
20 seconds jabbing
10 seconds hard punching combinations
20 seconds jabbing
10 seconds hard punching combinations
20 seconds jabbing
10 seconds hard punching combinations
20 seconds jabbing
10 seconds hard punching combinations
30 seconds rest, then repeat and repeat and repeat for as many rounds as you can. My coach typically waits until I am sucking in big breaths and then makes me do 2 more rounds. After this you know that you have had a workout.
When you are doing the 10 seconds hard punching combinations you are punching as HARD as you can. Here are a few combinations you could start with (I will assume you are orthodox and not southpaw):
Left striaght, right straight
Left straight, right straight, right straight
Left straight, left body shot, left hook
If you are not wanting to actually learn how to fight, hitting the bag as hard and as fast as you can should be fine for the 10 seconds hard punching.
In the 20 second jabs you don't want to give your opponent a rest but you need to get your breath back and set your opponent up for your next attack. Lots of moving and lots of jabs should be thrown in this time.
I realise that you arn't actually wanting to learn how to fight but you can give your legs a work out at the same time. If you just stand in one spot your arms will get tired but your body won't have actually had a work out.
Hope this helps you out. If you have anymore questions I'll be happy to answer them.