I first watched TMP when having an extremely limited knowledge of Star Trek. It was late 2005. I had to know what my father loved so much about Star Trek, so I devoted a great deal of time watching the films and the various series (mostly TOS and TNG).
One of my favorite scenes, which cemented Spock as being in my top 10 list of favorite fictional characters, was when he shot himself into V'Ger while only in a space suit. He then proceeds to non-chalantly record his findings.
Then there's Ilia, who has to be the most attractive bald woman I have ever seen. The probe, an exact replication of her, then emerged from a chamber in bare legs. I am a leg man, and she had a perfect pair. RIP to her actress. I found out recently that Ilia and Decker were the basis for Riker and Troi in The Next Generation.
The film has an almost creepy vibe, augmented by the fact that it is very visibly aged by today's standards. William Shatner provides the human aspect, when everyone else is oddly distant.
The twist as to the identity of V'Ger was very well done. The score, special effects, and timing of scenes, all masterful.