Try Anthem electronics, a division of Sonic Frontiers, if they still exist. A relatively budget line, fantastically well-built, 40 watts, had a phono stage as an option.
For a real budget set-up, try an Antique Sound Lab integrated, they sound terrific, with a tiny outboard phono stage for roughly $150 U.S., new. I know this is not built-in, but you can't beat it for the money, and it is tiny.