The most important consideration for adding new technology to a home computer is what the machine is used for. The best answer is not going to be the same for all people because home computers are used for a wide variety of tasks. The add-ons which are best for you will depend on if the machine is used primarily to surf the web, run a home business, share Ares music files, or play games.
If the main use for the home computer is web surfing, then the top upgrade should be to a fast wireless modem. Increased speed and portability would be welcome by anyone who uses their computer primarily for the internet. Adding on a good wireless router with DSL modem will cost at least $50 but it will allow you to access the internet anywhere in your home from any computer or mobile device. Plus it will allow you to use peer to peer networks and download and share large video files via software like Cabos.
If the home computer is used primarily to run a small business then the best add on is going to be a stand alone hard drive, which can be used to back up all of your important information. It is absolutely critical to back up all of your business files in case there is a crash and your files are lost. Many people share important files using programs like Amule from office to home and vice versa and you do not want to lose these files. An external hard drive with 500gb of storage will cost around $100.
If the home computer is primarily used for gaming then the top add-ons to be considered are extra memory and a new graphics card. To be able to properly play the newest video games manufacturers recommend at least 2gb of RAM and you can pick that up for around $40. The gaming experience will also be improved with a new graphics card. Most computers come with the Intel 3d Extreme Graphics card, which gamers agree leaves much to be desired. A better choice is the ATI Radeon HD 6850 which offers vivid colors and excellence, but comes with a high price tag around $200.

