If you have a small point & shoot you should be able to get decent photos in your local bar/pub if you’re very creative, can get really close to the band, use flash and can move around a lot.
A mid range digital camera will enable you to use an external flash which can improve the quality of your shots immensely. You will still find the larger gigs difficult though, as flash is usually banned. Nonetheless, some of the cameras with good zoom and image stabilising can achieve good results without flash. But for the big-name bands you really need a good digital SLR. Make sure you get a DSLR with low noise at high ISOs such as ISO 1600 and ISO3200.
Of course, film is still an option. But film is expensive and turnaround can be slow. Black and white film can be fun to use, ISO3200 works well and you have the option of developing it yourself in a home darkroom.
Below are some photos I took with a 3MP Panasonic FZ10 which is now old and very cheap technology: