Yes, FeedRead is a good approach. If the two sites are on the SAME MACHINE, it's even easier to follow. If not, it's still fairly easy (I just change what you install and where).
Basically, grab my PowerPack. If the sites are on the same server/account (needs to be under the same account/privs for this trick), install the PowerPack into your WP site (you don't even need to activate the plugins..), then you can just do a include of cg-feedread.php and call the getSomeFeed function with your WP site's RSS feed url.
If the sites aren't on the same server account, you still grab the powerpack, but in that case just upload the cg-plugins folder alone to your non-wp site's root (the whole folder, not just the contents, and not the plugins folder above it!), and again you can then direct-include the cg-feedread.php file and call getSomeFeed.
Read the feedreadReadme file, as it discusses the actual function call and parameters. Post here if you have any Qs.