I use PHP systems which are probably easiest for the beginner.
You will need to buy a webhosting package with PHP and mySQL database support. This will cost about £30 a year. These people
me2uweb - Internet solutions I have used for years. Buy the Ultra Bronze package with your domain.
You now need to learn how to with PHP connect to a mySQL db. Add a record, delete a record, update a record. Display contents from the db.
Also how to set up mySQL database.
I built one of these recently, I would do the whole thing for £(I have PM'd you a price) plus VAT inc the hosting. You can then put the addresses in one at a time via the admin or supply me with a spreadsheet and I will import in one go.