These days cheap, or even free, software can do a professional job of editing. The basic video software for Macs is iMovie and for the PC, Adobe's Première Elements is a good place to start. The more complex software available may give you more freedom and choice, but for the beginner these package can be overwhelming and very pricey.
Any new computer should be capable of editing film footage, and even a ten year old PC should be able to handle basic video editing software. Video editing takes up a lot of hard drive space, so keep your hard drive clear and get rid of footage your not using (but be careful not to delete footage you ARE using!). Investing in a new hard drive to store you video footage on is probably a good idea.
The output format will depend on it's destination. Highly compressed formats are best for streaming over the internet (Quicktime is the most universal), DVDs are great for send out to press and media, and a DigiBeta tape is need for TV broadcasts (something you'll need to get made up at a professional production company).