It'd be easier and more reliable to just call your ISP and ask them to give you a static IP address. The change should be reasonably quick (a few hours at most, mostly waiting for them to get to it). It shouldn't involve any noticeable downtime, and should only cost an extra $1 per month or so.
Your ADSL would be slow for this, though. Getting decent performance on websites is important, and difficult to achieve at the best of times, without the huge delays of going over ADSL. If your "customer" connected through ADSL and your site is ALSO on ADSL, then they whole roundtrip for communication will go over ADSL FOUR times -- over their ADSL out, over yours in, over yours out, and over theirs in again!
Even the smaller professional hosting companies are moving to well-connected, high-performance virtual/cloud hosting provided by big players like amazon and google and rackspace instead. Trying to get by on ADSL is at best an interesting experiment. Not that you should rule it out if the monetary savings are an important factor for you, of course.