First thing to remember is that your group is not alone. Even today there are paranoid individuals all over the planet that actively backup a variety of data that they think would be useful in the event of the end of the world. Governments also backup data for their own benefit, with agencies like the National Archives and Records Administration. As such anything your group fails to save, odds are someone somewhere likely has you covered.
The goal should not be to save everything, but enough so that scientists and engineers can fill in the gaps of that which is lost.
CNN reported that the average download speed in America broke 50 Mbps in late 2016. So I am going to assume that there are your group has multiple internet connections available for a total of 150 Mbps bandwidth. This means they will be able to download approximately 0.5 Terabytes of data a day till the end of the world (or until their cable provider decides to start throttling them).
Wikipedia is rather large coming in at 23 TB for everything in 2014. Good news is that compressed dump only the articles is around 12 GB. If your groups wants to download the compressed dump of everything they can expect it to be over 250 GB, but still doable in a day.
This will net you a lot of raw information on a wide variety of topics that can help scientists in the new world rediscover lost technologies.
Download Stack Overflow
The Stack Exchange is a very important component of civilization, it is something that must not be lost in the event of an apocalypse. Good news is that much like Wikipedia it is possible to download archives of it. The most recent one for Stack Overflow I can find is 14 GB compressed. Again easily manageable for a small group of people.
As scientists and engineers go to redeveloping lost technologies the various stack exchanges may contain the key answer they need.
Download other repositories of information
The internet has many repositories available for download. Ranging from the US Patent Office to illegal torrents of data dumps. Downloading scientific journals can get complicated very quickly, since there are so many of them covering a wide variety of topics and they typically require a subscription. They should get as many scientific journals as they can, but it should be the last item on their list, since it will be the most time consuming.
Persisting the information
If you want this information to last more than 10 years, you will want to store it on something besides a hard drive or solid state drive. M-Disc DVD and Blueray are the best option with a rated life span of a 1,000 years. The catch is they only have a 21 Mbps write speed. So if your group is in a rush they are going to need several writers to get the media burned onto M-Discs.
What Gets Missed
Government Classified Data
Since no one in your group is associated with the government I would like to hope that they do not have access to any classified documents (outside of leaked documents). Even though governments are not paranoid of an apocalypse, they do have contingencies for foreign nations striking hard at their infrastructure. As such they tend to keep back up copies of sensitive government and military data somewhere that will survive the end. The big gotcha though is that the most sensitive classified data tends to be stored encrypted, so even if it survives the end of the world, it will not likely be in a usable format by your group, but likely some other group will be able to recover it (like a group of ex-government agents).
Most classified data is not going to be relevant to a rebuilt civilization. For example information on the real names of assets and moles in Russia and China may be very sensitive at this time, but in a new era this information would become irrelevant. So if it is lost, it would not be that big. On the other side even if all the blue prints for advanced military and spying technologies survive (which is doubtful), the technology used to make them will likely still need to be redeveloped.
Corporation Proprietary Data
This information will likely be lost, but anything that would impact future civilization would be able to be redeveloped. This would include things like the process of making chemicals that are used to make non-stick coatings for frying pans to formulas that are used to index and search the internet.
People tend to care about their past. Knowledge of people's family tree and genetics would be lost. Lots of this information when lost cannot be easily recovered. This type of information impacts culture and thus can impact new civilizations.
In the end things will get missed, but with enough time they will be rediscovered.