Okay, so... Battlestar Galactica gets complicated because of all the miniseries and web series, etc. Netflix used to have the main series (minus one or two minor web series) and provided them in order, which made life so much easier. Sadly, Netflix took the modern BSG down, but you can still find DVDs at libraries, etc. So the answer to #2 is yes, there is a certain chronological order (though the web series aren't strictly necessary to watch, and they can be really hard to find). Technically speaking, there are two "movies" in this version (Ronald Moore & Gary Larson's remake), but they're really more of miniseries than anything else. That brings us to what you watched - if I'm recognizing the picture correctly, it's actually not either of the "movies," but the original/first miniseries (technically two episodes, but they can be watched in one sitting pretty easily) that served as a pilot for this remake of BSG. So you did good for yourself on that count - that original miniseries is pretty much essential to understanding the rest of the show.
So, you've watched the kick-off miniseries - now how should you proceed? The four main/regular seasons are a good start. Then there are the "movies"/miniseries. The first one, Razor, belongs in there shortly after the Pegasus storyline - you'll recognize it when you see it, but I don't want to give too much away. Then there's also The Plan, which shows you the first few episodes (original miniseries + a good chunk of season 1) directly from some of the cylons' perspectives. I personally didn't watch that until after I watched everything else - pretty safe spoiler-wise that way (I'd advise that you at least don't watch it until after you've watched the first season of the regular series).
As for the web series - there are three. The first, "The Resistance," is probably best watched during or just before Season 3. The other two - "Razor Flashbacks"* and "The Face of the Enemy" - are probably best watched once you're already well into Season 4. For a relatively spoiler-free account of season/episode/etc. order, you can look here. At least, it gives you the dates of when each episode, etc. was written and produced, and despite that it all looks like a jumbled mess when you put everything together, pretty much everything was written/produced in chronological order, so... I hope that was helpful. Good luck, and I hope you enjoy BSG!
(P.S. Caprica is also a fun spinoff of the series - it was cancelled after only one season, but it provides some interesting origin stories. So, if you like BSG after you've watched it, definitely go watch Caprica!)
*You may be able to watch this one earlier, especially as it's largely based in flashbacks to events from way before the series even started, but seeing as my memory is a bit foggy on those episodes, I don't want to give too much advice in that particular area.