Best Practice: Table, Div, List or some combination...?

Lists are for lists, tables are for tabular data, and divs are for layouts. So if you want to go the best practices route; I think you should be using a table here.

That being said; using divs as opposed to tables isn't all that bad. I wouldn't worry about rewriting if you're already using divs instead of a table. The one caveat being you're clearing your floated column divs. ex:

<div class="row">
  <div class="column" style="float:left;"><!-- Some stuff --></div>
  <div class="column" style="float:left;"><!-- Some stuff --></div>
  <div class="column" style="float:left;"><!-- Some stuff --></div>
  <div style="clear:both;"><!-- Leave empty --></div>
</div>

What you should avoid is the opposite (using tables where divs should be used).

Also, even though you may be able to get some kind of table structure using list elements, this is NOT the route you want to go. I've never done it before...to be honest out of the hundreds of examples I've looked at I don't think I've ever seen anyone use them for such a purpose. I guess the best reason here is why would you? Since I've never seen it before I don't have any examples handy which illustrate why you shouldn't do it. But to me this is akin to telling someone not to use a pipe to loosen a bolt when they have a wrench handy. I mean sure....maybe the pipe could get the job done but the wrench is right there...

In this case a table is fine. Tables are for displaying tabular data, like a row in the db. You should avoid using tables for page layout though....

As for having thousands of rows, you may want to look into pagination. I don't think there is a better "best practice"

Realistically, you can use any container you'd like. Best practice is to use the elements for what they were meant to be used for. If you are displaying tabular data, by all means use a table! There are great plugins to make the experience for the user better, and it's really easy to read and copy/paste.

The question that I always ask myself is if that data would be best shown in a Word or Excel file. If Excel, then it's a table. If Word, it's div's.

If you're using thousands of rows you'll probably want to give the user control on sorting, filtering, and pulling in more information to aid usability. I'd use a table with some jQuery plugins like tablesorter, hovertable and tableFilter to help make this easy.