Before the iPod came along, Sony was the best maker of portable CD players, with their Walkmans. I would pick one of the later versions of Sports Walkmans on ebay. They contained significant buffers that could store enough music signal to ride through the skips, even while outside and jogging/running. The later ones were compatible with CD-Rs and mp3 files, while the earlier ones were not. The S2 form of CD Sports Walkman were among the latest versions. I have had a couple and they are really quite good. This is an example for less than $20: https://www.ebay.com/itm/Sony-D-NS505-S2-Sport-Discman-Portable-Walkman-CD-Player-Radio-Tested-Working
Aiwa portable CD players were among the best. I still believe Sony was the best, but many Aiwas were right up there next to them. I have an early Aiwa sports CD player. Other than being a bit bulky (it was an early model in the sports CD player evolution), it's an outstanding device.
Sony bought Aiwa, so maybe they recognized the quality.