1 gb RAM is indeed enough to run Windows 7 32 bit. If you have a screen resolution problem then try a few things first before panicking and retreating to an almost-XPired OS:
Go to the Support Downloads website for your computer model or video card, download and install the Windows 7 or if necessary Vista/XP driver for your graphics chip or video card. You may need to run the .exe file for a Vista/XP driver in Vista/XP SP2 compatibility mode by righclicking .exe for the Compatibility tab.
If the .exe for the various drivers you try only unzips the drivers, then go to Device Manager>Display Driver>Update Driver>Browse in the drivers folder until it picks up the driver.
Make sure you try each Screen Resolution for any drivers which will work until you find one that works. Then if necessary change the DPI to increase font size if sharper resolution results in type which is too small. I typically run highest resolution to get sharpest images, but increase DPI to 117-125% to make it look right, then run Internet Explorer at 125% zoom for perfect sizings.
If you would like more specific help on your video drivers, then please update your video specs from "old card" to the actual model and we will help you find the drivers, or post in the Drivers forum. Let us know any other issues we can help you with as Windows 7 runs fine on many 1 gb RAM computers.