404, 301 or 410 responses for GoogleBot

What does google bot prefer?

[Bewenched]

We have several pages of products that we don't offer any more and up until recently we just turned off the products so it couldn't be purchased and left them on the site.

We use google sitemaps and have for a long time so all the products that are still available are the only ones listed in the maps.

I first implemented the 404 Not Found
Hoping Google bot would quit hitting the page and indexing the turned off items and go on to available items, but it just kept coming back and errors kept showing in sitemaps web crawl.

404 (Not found) Annoying to see so many come back with that error .. makes me gasp thinking something is really broken on the site. Note .. these are not in the sitemap anymore.

Should I be useing 410 (Gone)?
Should I use a 301 (Moved Permanently)
and point the end user and google to a more useful page or a search page or would that mess us up in the SERPs?

We've had a hard enough time as it is this year with all the search engine changes.

[Just Guessing]

googlebot seems to treat a 410 the same as a 404 - refuses to believe you actually mean "Gone", and keeps coming back looking again.