No one said (or, at least I didn't) that a budget system can't be enjoyable. But let's not forget the ancillary stuff necessary for it to *be* enjoyable-especially relative to a ceedee reference. Stylus brush. VTF scale. Record cleaning brush. The tools, knowledge and discipline to learn to align your cart. Some way of cleaning the records, particularly if the OP is planning on buying used. LPs are valuable, so some good sleeves for storage. Oh yeah, that brings up the pesky issue of software-how much of that 400.00 budget will go to buying some music? A library of, say, 12 albums is going to get old really, really quick.
Yes, people have been enjoying records for close to a century, but how many of those people would choose ceedee over vinyl on a mid-fi system? Who knows, but if the marketplace is any indication, about 99%-and as much as I like vinyl, I'd probably be in that percentile. If I was in the OP's position and was gifted with a large record collection, it would be fun to buy a cheap record player and spin some tunes. But I'm pretty sure I'd go back to digital for the best sound.
And that was, after all, the OP's initial question.