You're probably on the right track to build around an amp but a Class A/B amp and 350 Watts seems more like a boat anchor than a flagship.
For that money I'd probably go with the Coda #16. Similar power but the first 100 watts are Class A (up to 300 watts into 4 OHMS).
I would be hard to build around speakers as I'd hate them until I got something to sufficiently drive them but the amp should be purchased with a speaker in mind.
I'm torn about vinyl. It does sound better but the hassle involved with cleaning, storing and acquiring the music just makes me question my commitment. to the hobby. I shudder to think of having to get up and turn the album over every 15 minutes. I'm sure I have several hundred albums saved from pre CD era That would be cool to listen to again but my musical tastes have changed since the 80s and finding excellent copies would be pricey.