Just a quick list of equipment some of us on budget could start with. (all prices at the time of writing.)

Good budget audio

Shure SM58 is the most popular stage vocal recording mic. It is a good mic to have for home recording too. Easy to handle and record, at a very affordable price, this is usually the first choice of most musicians starting to record.

Audio Technica AT2020 (USD 69) – condenser microphone

USB Version of the same mic: Audio Technica AT2020USB Studio Condenser Microphone is one of the best options at USD108, if you want to connect the mic directly to your computer through the USB port, without buying or using an external audio interface. Audio-Technica ATR2500-USB Cardioid Condenser USB Microphone ($47) is a cheaper USB mic option.

Zoom H4 Handy Recorder is used by many pro sound engineers because of its compactness and ease to carry around.

Audio interface

Focusrite Scarlett is an affordable audio interface(USD 127) which allows very high quality audio recording. 

Software for recording

Audacity software sequencer – free

Reaper is a highly acclaimed software sequencer with tons of useful features. The trial version is fully functional. After 60 days the user is prompted to buy a license for just USD 60. There is no limitation imposed on the user by means of technological restrictions. A very good option.

Search for free vst instruments and effects.

Good budget Video making

Many of us make documentaries and do other video related work. What about good cameras?

Chappa Kurish is a good full length Malayalam movie (direction: Sameer Thahir, camera:Jomon T John) shot entirely with canon 5d and 7d. There are a few other good cinematographers who use such cameras for street and crowd scenes.

Canon EOS 7D 18 MP CMOS Digital SLR Camera with 3-Inch LCD (Body Only) costs $1499

Gopro Hero 3 Edition ($400) is another camera you may want to check out. (Thank you Shahid for pointing me to the video)

When you find a good list, please feel free to post in the comment section below.