ZDoom

I'm going to confess something: I've never played a single Castlevania game. And as someone who loves Metroidvania, I sort of hate to admit that. That said, I have been meaning to get into the Castlevania series, in particular the Metroidvania-style titles.

Now, the exact question is as follows: out of the GBA and DS Castlevanias, which one would you people say is the best entry point into the series? Why only the GBA and DS games, that's because I don't own a lot of consoles, and those two platforms are pretty much the only choices I have. I don't want to emulate the games either, mostly because I prefer to play console games on the actual hardware (unless less favorable circumstances force me to emulate them), but also because I have concerns about the legality of emulating games I don't own physical copies of.

I do have a PS1 as well, but Symphony of the Night is not an option for the reasons stated above, as well as the utterly ludicrous prices it commands on the second-hand market.

Thanks in advance.

Definitely grab the 3 GBA titles. Aria of Sorrow is by far the best CV on the GBA, and closest to SotN. I haven't played the DS titles.

I would say Aria is the most approachable, though Portrait is my absolute favorite of the bunch. Harmony is less good but still good, Circle of the Moon is just weird and hard, and I found Dawn to be a bit sterile and formulaic compared to the others. Ecclesia's a good one, but it does a lot of stuff differently from the others, and doesn't always succeed at that.

Circle of the Moon is hard, but it's also got a fantastic soundtrack given the hardware. It's still worth a play through, although on the original GBA hardware, you might have a difficult time seeing things due to the darker palette used.

I actually broke this down for a coworker once, Castlevania games are divided into "Pairs". I noticed you said you were biased towards Metroidvania installments, thought I recommend a slightly different approach to maximize your enjoyment if you want to get invested.
Outside this are a couple strays: Lament of Innocence and Harmony of Dissonance.

You do not want to play any second game in a pair first, because it makes the other one harder to enjoy.
Additionally, you also do not want to play Lament of Innocence, Aria of Sorrow, or Rondo of Blood first, because all of their plots require familiarity with the universe to fully enjoy. I also recommend playing Lament before Aria whenever you do come around to them.

A good (my favorite) starting point is "Chronicles" on the PS1, due to it being a mostly-straight remake of 1 with an optional easier "Arrange" mode. (I say skip "Super IV" entirely until you're familiar with the series, or play it absolutely first. Another good starting point is Harmony of Dissonance, because it doesn't really fit into any of the mentioned "pairs". Circle of the Moon is probably the third best option, because it introduces you to the setting without expecting you to have suppositions. (Iga wrote it out of canon officially, so it works largely stand-alone, but it pairs well with Ecclasia due to the content and themes)

It's a series I love alot, so I apologize if this is a bit of an infodump. Given your console limitations, the three starting suggestions I have are all available to you, as well as the NES games and Bloodlines recently getting re-released on Steam, leaving the PS2 games and Rondo largely your only missing links. The 64 games are non-canon officially and don't add to the timeline, but I personally love them and find them to be the best of the 3D titles when it came to gameplay.

I prefer the older style of Castlevania games, but Portrait is my favorite of the metroidvanias.

If you happen to be able to access a PS2, you absolutely should not sleep over Lament of Innocence and Curse of Darkness, COD in particular is my favorite of the "Metroidvanias".

Otherwise, I can simply vouch for Aria of Sorrow and Dawn of Sorrow.