I'm assuming this is an OAV series with movie sequels...?
Grappler Baki is a very, very long running manga series, very little of which has been released here, so my understanding of it and how the anime adapts it is a little limited, but here goes (this is going the be longish):
There's an original OVA called "Grappler Baki" which takes a small section of the manga released here called "Baki the Grappler" and animates it. It's pretty much mostly just 2 fights and a tiny bit of plot to tie it together. As already mentioned, this is mostly just a fanservice OVA for people who have read the manga. This has been out for a few years now and you'll notice Baki's design is quite different (black hair, smaller frame and lots of scars). If you're interested in the manga, it was being published in Raijin Magazine. Sadly the collected volumes never got released and Raijin has pretty much folded, so you're kind of out of luck on that.
Now what you probably saw in the store was the newly released TV series, titled "Baki the Grappler" like the manga. It ran for 2 seasons and I don't think there's been anymore. The first season starts out (if my memory is correct) when Baki is 12 years old (taking place before the events of the OVA) and goes though his training during his teen years. The second season (I think they're just releasing it as one big show here) changes the style a little and switches gears from Baki growing up to being one huge tournament, injected with various little backstory bits about his father. In the TV series, Baki changed quite a bit from the manga and OVA. His design is a changed to make him a little more handsome, with red hair and no scars. His body size also changes during the series to reflect his age and such which is a nice touch. He's also not as fun loving and is much more serious and somber. There was a sequel manga in Japan, and I believe that's what the TV series is based on.
Anyway, to sum things up: The OVA is fun, but unnecessary. Most of it is later covered in the TV series anyway (although with a different style and mood). It's worth a rental to watch the fights.
The TV series on the other hand, is worth a purchase. Season 2 feels a little long since it's mostly just fighting, but Season 1 is excellent and even though it's over the top often, it feels realistic and brutal with some excellent characters. It's also fun to watch the character grow without huge jumps in time. That's something you don't see often in anime. It does have some jumps though. There's a HUGE jump between seasons which kind of sucks. Dunno if those events have been covered in the manga, but like I said it's a VERY long book, so it's easy to understand why they had to skip some stuff.
Hajime no Ippo? I'm assuming the rights haven't been bought? Do you know where I could get fansubs?
Ippo's been licensed and there's a few volumes out now with 5 episodes per DVD. The name has been changed to "Fighting Spirit" though. Ignore the generic name, the show is fantastic.
It's over the boarder street fighting and a pretty good story that eventually (like alllll fighting anime) transforms into a tournament fighting thing (s2). By then you've watched Baki grow up and fight all types of different styles. Can't tell you any more than that Baki's dad is reason enough to watch this anime. 