Many people start out with a suitcase player and then upgrade to a better turntable later. Although I don't recommend them, generally they're OK as long as your expectations for sound quality are low -- they're not going to "destroy" your records (that's a debunked myth), but the built-in speakers sound weak and tinny.

It'd be better to start out with something like the Victrola Eastwood, which is about the same size as a suitcase player, but has an Audio-Technica magnetic cartridge, diamond stylus, and properly counterbalanced tonearm, which will be less likely to skip on bass-heavy records.

Adding a pair of powered speakers will make it sound a lot better, and would be a good first upgrade, because you'll need them anyway once you eventually get a higher-quality turntable which doesn't have built-in speakers.

The $90 Victrola Eastwood.