It will depend on what kind of quality you want to offer the customers and also on how fast they want their prints. Also consider how much customers are willing to spend.
Whether you print them on the same day so that customers can get their prints within a short period of time after having their photo taken or whether you decide to do the print job later at home and mail them out to customers, this approach will ensure customers purchase the photos. If you were to upload the photos to an online gallery such as Photobox, are you planning to charge customers for having their photos taken during the event and then have them spend money a second time for ordering a print from Photobox (something they might not want to do)? And if you don't charge them during the event and expect them to 'donate' money via purchasing prints from Photobox, what happens if they don't order prints? You could end up having wasted time and effort.
As for buying a printer:
1) This charity event, will you be able to set up a booth that is close to a power outlet? If so, you could just get a good low cost photo printer that can do up to A4 sizes, connect it to a laptop and set up your booth. Take into consideration of paper and ink costs.
2) Canon has some good compact photo printers, i.e. their SELPHY series: http://www.canon.co.uk/For_Home/Product ... index.aspx
They can be powered by both an AC adapter or a battery pack you can purchase. I have never used one myself so I am not sure about the quality, perhaps other members of the forum or DP staff can advise.
Another thing to consider (if you want to offer the prints during the event): are you going to be working alone? It's not going to be easy if you're doing the photography and the printing on your own, better to get someone to handle the print job while you concentrate on the photography. Especially if you receive many customers throughout the day.