Don't waste good money on diaper genie's and special diaper disposal systems. Start saving the plastic bags that newspapers come in and when you have a stinky diaper, put it in the newspaper bag, tie a knot and put it right in the regular trash. Make sure to carry some in the diaper bag also for when you are out.
Baby wipes are your best friend. Put them in plastic bags and stash them everywhere. Put some in the car, in your purse, and in the diaper bag. As a new mom I have used baby wipes to clean not only bottoms but faces, fingers, carpets (great for cleaning spots left by dripping bottles and urps), bathrooms (I'm not sure if that is very thrifty, but on a new mom's limited time schedule, if I didn't grab a baby wipe and clean the bathroom, it might not have gotten done.)
Also, if you have a two story house make sure you have some of everything on both floors so you don't have to run up and down. We were lucky enough to be given two cribs by friends and had a second crib in our living room until the baby was about a year old. Not only can you keep an eye on them but they get used to noise.
1. If you are a first time mom, don't let other moms tell you all their labor room "horror stories". It will only make you over anxious about something that probably will not happen to you.
2. If you are bottle feeding and have that 2 story house mentioned above, a good thing to have is a bottle warmer. Then when the baby gets up in the middle of the night, you don't have to stumble downstairs to the kitchen to warm a bottle.