I need to delete some messages in my folder to free up space, but I would like to save some of them and am not sure how best to do this. What is the quickest, easiest method? Thanks.

If you scroll down to the bottom of the folder you want to save (i.e. your inbox), there are 3 links to download your messages from that folder: XML, CSV, or Text.

XML is a 'universal' way of structuring data and is easy to move about and import into other programs (ie Access, Excel, etc...).
CSV stands for Comma Separated Values (each field like who sent it and the title of the PM are separated by commas). CSV files can be imported into programs like Excel and can also be imported into other programs, but that type of support is fading (XML is the new CSV).
Text is just plain text. Not too pretty to look at, but easily readable.

Why not try each of them to see which way works best for you.
Also remember that Premium Geeks get about twice the PM storage space (shameless plug )

Hope this helps