A good brand of a record player, such as audio technica in a more expensive model, or another good model at places like F.Y.E (For Your Entertainment) would be a wise option. I would recommend getting the record player at this store, for virtually all of their brands and models they sell in those brands are great and play well.
As far as the weight of each record, generally the heavier the record, the better the audio because the grooves are bigger, thus the record needle reading the grooves has more "accurate space" to, well, read the record and not be as compressed. A good weight is probably less than a half a pound, but this is just an estimate.
However, no matter what the weight of a record is, this usually won't have that much to do with the sound, unless it is a really skinny record, for instance, that was made with digital equipment. This usually sounds better than a CD, but not by THAT much.
Records (vinyl, for that matter) have better audio quality than CDs because they are less compressed, and the needle is making accurate, physical, "uncompressed" contact with the physical grooves of the record. And with the right speakers, record players can sound extraordinarily pleasing to the ear.
Best of luck with your purchase, and I hope this helped.
experience with vinyl for nearly four years