Agree with above that Sea Chanteys as work songs were often unaccompanied; basically the chanteyman himself was there to set the pace of the work - so the chantey iteslf WAS the accompaniment.
But yet, performances of sea chanteys and other folk songs go well with the concertina.
I also agree with the above, not to purchase the cheap asian imports. I bought an asian 30 button anglo online several years ago before I knew what I was doing, and was glad I had purchased from a reputable store so I was able to return it, because the quality was so poor. I waited another two years before I got my 20 button Anglo. I love it, but I do wish my budget allowed for a good 30 button. The Rochelle anglo is what I would recommend too. The reason I didn't buy one was because of the size and weight, as it is a bit heavier than the $2000-$2500 anglos out there. But you aren't going to get around that within your stated budget, unless you search for a good deal on a vintage 20 button anglo like I did. If you decide to upgrade later when you are ready to spend more, several places take the Rochelle model back in trade, often at full price, if you are purchasing one of their better instruments.
The 30 button anglo will play more than just two keys. The 20 button already plays effectively in two keys (and the relative minor keys for each) and even that can be stretched into other keys if certain notes are not required , but the 30 button gives you quite handful of additional useful notes. For example the C/G is often used for D major as well, and many other keys are are possible, just not quite a easy, as I understand it.
Some say the anglo was considered more of a working class instrument than the english concertina, but that isn't necessarily so. If it was true it would suggest that the anglo would go well with sea chanteys. In any case I know of several good chanteymen who do perform with anglo concertinas.
I do have a good musical background, and play several other instruments, so the limited keys on my 20 button anglo do annoy me at times. I wonder sometimes about the english system with all the notes and no worries about bellows direction, but when I tried one I didn't care for it. (and that was before I had started learning the anglo system either) Alternating sides from one note to the next just didn't match my way of thinking, although I've seen others that seem to enjoy it very well. I also didn't care for the way the english is held; I found the thumbstrap and pinky bracket very uncomfortable. Again, others seem to enjoy the english concertina very well.
I am intrigued by the duet systems. I think that might be pretty good, but you aren't going to find one in your price range, and it is hard to find good instruction material for these systems, particualarly as a beginner. There is the concertina connection Elise model, but from what I read, it has too few buttons, and the missing notes compromise the flexibility in keys that the duet system is supposed to offer. Maybe someone who has tried one can say more about that.
I strongly recommend trying out several intruments of each type before spending any money. Make the trip up to Button Box. I've never done business with them but they appear to be well respected, and clearly have a variety of intruments on hand to try, which is exactly what you need. Try some of the more expensive instruments as well, so you have an idea what the difference is. It will make you pine for them, but you may as well learn on the system that will lead you toward the instrument you hope to upgrade to later. Amherst is a nice town to visit too. I have been there, although I didn't play concertina at the time, or know about Button Box.
Back to sea chanteys! The best way to get involved in these is to find other people that like to sing them, as these are call and response songs, and only really come into their own when sung in a group, not as a soloist. I don't know what there is close to you, but there likely is a group that gets together somewhere nearby, the trick to find them. In June there is a Sea Music festival at Mystic Seaport You really owe it to yourself to get there, if you hadn't already planned on it!