Well, there's a bit to unpack here.First of all, the theme of the older games has been an insane arena shooter that was also a "walk backwards while holding the fire button" simulator. If you still end up liking it, Siberian Mayhem will be extremely fun. If you end up liking that game too, try Serious Sam 4. If you happen to like these games too, then try Sam 3. So, I suggest you start with the encounters (HD or not - up to you).
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Siberian Mayhem is basically improved, shorter SS4, so it may make no sense without knowledge of the story but is probably the best Serious Sam content we got since The Second Encounter. But as long as you stay outside of buildings the game can look awesome, and the gunplay is imo the best from the series, every gun feels extremely satisfying to use. Serious Sam 4 tries to go back to that silly humor but kind of overdoes it, and has A LOT OF CUTSCENES. Serious Sam 3 is VERY realistic, less colour, more realistic enemies, tactics, weapons, and less dumb humor. Even then they take on a more realistic approach only with silly jokes here and there. Most similar is probably The Second Encounter, which has various levels with differing color schemes, but for that you'd need to start with TFE.
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Serious Sam 2 has a VERY cartoonish style.