is really down to in most cases more on what you like rather than have to follow an order or a certain watch order. It's why people have different recommendations like whether they like action or want something more tamer. A majority of the series is episodic with only the later series starting from Part 4 having storyline episodes. There are some entries that do require better knowledge of the series than others and in rare cases may have two parters or a continuation (even Part 2 has a flashback to Part 1). It's why personally wouldn't recommend Part 5 to a newcomer just on the grounds of fan service and multiple connections but many people have watched Part 5 as their first entry, it does introduce Albert and Yata though, the latter appears more in the new stuff.
The goto gateways in the past have been: The Castle of Cagliostro, Episode 0, The First and series wise Part 2 (classic Lupin) and Part 4 (modern Lupin)
Since you already started with Part 2, you already have a fair idea what the characters are like with the exception of Zenigata who in other entries may be more competent. You can stick with Part 2, just to prepare that only 81 episodes have an English dub. For modern Lupin series, Part 4 as mentioned introduces the storyline episodes and takes elements from various series making it its own but even then probably take a few more episodes to get the feel of the characters. After all the opening of Part 4 isn't the best to know what the characters are like and has a misconception that gets resolved later down the line.
(While I would also recommend Part 1, it is a series that is showing its age and the first episode can be a turn off. It just depends whether they can watch early 1970s rougher looking animation in terms of style and am in two minds whether to recommend this to a newcomer or ones they got into the series more. There are some great episodes though and it is later on the series an early work of Hayao Miyazaki and Isao Takahata while earlier episodes are more closer to the manga. Yep. As a note; only Parts 1, 2, 3, 5, Lupin Zero, the OVAs Lupin Family Lineup, Return of Pycal, Is Lupin Still Burning and the TV Special Alcatraz Connection have some ties with the manga whether it is adaptations, references or characters. There's probably a few that I missed out. Just mentioning this as unlike a majority of manga to anime adaptations, the manga is more forgotten outside of Japan and is more questionable.)
For films The Castle of Cagliostro has been for many people their first Lupin, as a warning it is tamer than the majority of the series but watching this does help with the many references and throwbacks in later Lupin entries and other anime/TV series/films too. It is also a Miyazaki film so you get that great animation and people do include this with Studio Ghibli watches (along with Nausicaa but weirdly not Panda Go Panda, a Miyazaki-Takahata two film series by Tokyo Movie). While personally I have yet to see The First, it does make for a good first entry in terms of the series and more tonally closer with the only downside being one of the few 3D CG anime in the entire series and the best animated one too. Both The First and Cagliostro introduces for a newcomer "the girl of the week" where it focuses on the female lead for the film/episode, a typical plotline that pops up in the series especially in TV Specials even if Part 1 does technically introduce this plotline first. Episode 0 is another movie and a good TV Special for a newcomer, it's even an "origins story". The TV Special concept while isn't unique to Lupin is a part of the series identity. Lupin has a lot more TV movies than theatrical ones and you get different recommendations depending on who you ask literally. Episode 0 is one that gets mentioned the most.
I would also recommend The Mystery of Mamo. Usually people recommend this one a bit later into the series but thinking about it... People recommend Cagliostro and that's different compared to some Lupin entries as good as it is, while Mamo may be more wild is still more of what you expect from Lupin. Bearing in mind "typical Lupin" is usually in between Mamo and Cagliostro in terms of behaviour. It explores the relationships of the characters, it has a great villain, it has a deep plot line especially for the 1970s and has some decent animation too. It also makes it easier to prepare for the tonal shifts that the series does from time to time but if you carry on with Part 2, you get that as well. Plus Mamo took some stylings from the manga and was Monkey Punch's favourite. It was also a gateway for many of the earlier anime fans because it was the first movie, even the English name came off from a really old school anime fan (just because he didn't want to call it Lupin vs the Clone). Another bonus it is rewatchable especially with the bonus of 4 English dubs!
There is also a spinoff series called The Woman Called Fujiko Mine and in the same lines Lupin the IIIrd OVA series (Jigen's Gravestone, Goemon's Bloodspray, Fujiko's Lie; all of these follow on from each other). These are more mature and hardboiled than the mainline series. Even between TWCFM and Lupin the IIIrd have their differences. TWCFM is also almost an entirely storyline focused series, some people do recommend this but it's not for everyone... The OVA series though is still recommended (with a caution though). Lupin Zero is also a spinoff but tonally different and is not part of these series (does take a few cues from the manga though).
As for sub or dub, in most cases it is personal preference. With the series, sadly not everything is dubbed and some of it are early dubs that have issues of the time with the worst offender being The Fuma Conspiracy. Fuma also happens to be one of the very few entries that also has a different Japanese cast than the usual. Then there's Part 2 where the English dub in places is more of its own thing. In terms of content it goes Japanese original -> Italian dub (most of the series outside of some more obscure entries, because Lupin was popular in Italy) -> English dub -> most other dubs. Each have their own advantages and disadvantages like if you're bad at hearing, subtitles but if you have problems reading text then dubs are the option. Modern dubs (Part 1, Part 5, Part 6, Goodbye Partner, Prison of the Past, Episode 0) are really good though and differences are usually down to lip-sync. There may be some lines changed here and there but generally stick to the original script. Also as a plus, the current dub cast is just as praised as the Japanese cast so you're in good hands. It's not to say the other cast are awful (the Streamline, Funimation and Lupin the IIIrd dub cast have their moments to shine)...
The exception is Part 4 due to some complex licensing where the English dub was based off an earlier incomplete version of the anime while the Japanese version is considered the final. While you can still watch the English dub and be able to enjoy it, the Japanese sub has animation fixes (especially episode 21/20 JP version), has an actual animated intro/credits and has the Lupin music (the music in the English/Italian versions is different). Also the dub version was rushed out so it may not have the expected level of polish, still good all things considering.
A warning though if you do go to the sub option, not everything is subbed well because not all Lupin entries are licensed and in the case of the Part 2 Crunchyroll subs after episode 79, they were based on a script dating back to the 1980s so expect typos, lines that make no sense, skipped lines (applies to Part 3 too), mistranslations and not having the nicknames that we known (Pops for Zenigata, Fujicakes for Fujiko). Even the Discotek subs that are basically the best have a few translation issues and typos to watch out for. Part 6 has a good sub too.
