Well... you should be aware of the huge differences that will occur when such a craft crashes down to earth with a huge load of civil observers either in country A and in country B. And it will be completely different in country C.
So while the most common place for alien-actions (the USA) may have a plan for stuff like this happen, many other nations are not prepared for this. For example in Germany a spaceship that parks itself in front of the Bundestag (where our chancellor is dwelling around) will most likely receive a traffic ticket for not owning license plate, dangerous intervention into air traffic, parking at a disabled parking location and piloting a not TÜV-approved (TÜV forbid you to use your car if its a piece of rubbish) vehicle without a flight license. Further, the aliens may get a lawsuit for illegal immigration and running around naked in public.
But in your case you claimed that this was a crash. And its clear that everyone who did observe this did notice. So the case may develop different for they following major cases:
industrial nations: Will deploy police and fire fighters and other emergency agencies, lock off the place of happening and trying to determine whats wrong with that stange plane. As soon as they notice that its extraterrestrial maybe their army will try to grab all the pieces and lock em away. Most likely, some time after this mutual allies, that will got news from all the civillian spectators, will be allowed to participate in scientific research of this. Meanwhile, the whole world can watch dozens of videos of the crash on youtube.
emerging nations: May act in the same way, if the crash site is not in a desert, rain forest or tundra. In these cases some military spotter will go out and you can skip directly to "grabbing whats left", but without "sharing with allies" maybe. Civil reporting will drop sharply when you hit an area with low internet access at all.
poor nations: A local spectacle, where a bigger nation may approach and offer "technical help", in case news travel far enough. Maybe all who did observe think it was a sign of god or something like this and carefully avoid interfering with that thing any more. When you hit a "rouge nation" chances are good that they will get the leftovers and being able to profit from this in a way that makes them a global player after some years. Don't expect any footage beside some wild shaking ones.
So... these are vague estimates. Like said before, it depends where that space ship (and the pod) did land at the end. If you want an agency to pop up and take things in their hands, you should crash that ship somewhere you know a superior intelligence service is working and a big budget is available to spend to such agencies. Russia, China and the USA of course, Europe, India, Japan, British Commonwealth as secondaries...
A global working group... oh dear, just claim Illuminates are active again. At all, they even made it into Deus Ex as a group of global rich people, so just throw together some of the more influential companies which may share a common goal and give them a Joint-Venture private security force. And for some goodwill, all your crash-events did happen close to one of their companies. Or better: right on the parking spots for their employees.
But if you are after a government agency that may get in charge of the crash-site anywhere, UN and NATO may be your group of choice. Otherwise you will spend most time doing diplomacy, which can get pretty boring.
If I could choose the landing-sites... I would place the pod at Antarctica and the UFO somewhere halfway between Europe and the USA - maybe at Iceland (which is not halfway, but... well) - so that every big player get the chance to be there first, while the local authorities are unlikely to be prepared for such a happening. Some of the Oceania-Islands (Java!) may be a good spot too: quite big cities available and most big players within two hours recon-plane-range.
At the end... when no evidence of dead alien creatures from the inside made it to the internet, a country or company will try to claim that this is in fact an earth-bound plane which happens to... well, they shouldn't have updated their flight-computer to windows 10.
Otherwise it will be a matter of hours before to much evidence is around to conceal this any more. Just take group of students with smartphones and a nearby 4G Phone Transmitter Station...
I feel like I did miss something, but maybe it pop up in my mind later... or somebody else does name it.