Congrats! I'm in a similar position, recently acquiring a 4k player myself. I've been assembling discs as I've come across deals. Movies which I think really benefit from the 4k treatment include:
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Lawrence of Arabia. Ideally, the first time anyone sees this movie would be on an IMAX screen. My first viewing was with 720p DVD rip watched on a cracked tablet screen, and it was STILL visually impressive. Watch it on a scale commensurate with the story itself, and it's quite possible some sequences will take your breath away.
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The Magnificent Seven. Similar vein as Lawrence (sweeping widescreen shots of desert locales), but a little grimier. The whole image has this really lovely texture and vivaciousness to it. I particularly enjoy the latest releases new color grade, which lends further vitality to the picture, emphasizing the panoply of color in many scenes through increased saturation and dynamic range. It does not tread into cartoony, Technicolor excess though, instead feeling "just right" to my eyes. Like how I remembered the film looking, rather than how it actually appeared on my old DVD release of the movie. --> Addendum to the above, the Criterion release of Seven Samurai is also worth picking up. It a perfect example of how good an "old" black and white movie can look.
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Blade Runner. It's a movie driven by vibe and aesthetic as much as plot, if not more, and the clarity of an HDR 4k picture enhances those features. Those aerial shots of LA, where you can see every little detail of the miniatures, down to each individual window of the Tyrell megastructure, are, again, breathtaking.
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Alita: Battle Angel. A 21st century update of the cyberpunk aesthetic, but looked at through the maximalist lens of anime/manga, as opposed to the brooding noir tone of the Blade Runner. I don't know when the next time we're going to get Jim Cameron levels of production value in a cyberpunk setting any time in the near future, so I appreciate being able to pick out all the little details in the background of the frame, as well as the heightened impact of the crystal clear action sequences (thinking of the rollerball death match race sequence in particular).