Most accounting software (the newer versions, at least) won't hog much of your system's resources, but you should check to make sure that it is compatible with your computer's operating system. See our Comparison Chart for system requirements. If you don't want to download software, there are a number of free online services you can use to track your finances; see our report on personal finance sites.
Some companies offer a mobile app so you can check your accounts on the go. SplashMoney has the widest selection, with an app available for every mobile device from BlackBerrys to iPhones. YNAB has mobile apps for iPhones and Android devices, and for the Kindle Fire. Quicken does not have any apps for mobile devices, though it shares a parent company with Mint.com, which has a free online service and well-reviewed apps.
Experts agree that a personal finance software package should, at a minimum, offer the following functions: