Calculating the storage needed for all photos

This could help:

https://photo.stackexchange.com/questions/56069/how-can-i-determine-the-amount-of-disk-space-used-by-my-lightroom-photo-collection

I'm also not sure that I understand your concerns correctly.
One goal is to clear up the "mess" and find a better approach for the future.
In addition to the one already mentioned, it is important to consider how e.g. the images and catalogs can be protected against loss.
It is advisable to differentiate between backup and archive, because these are different concepts.
A backup can e.g. be a copy of a work progress.
An archive goes far beyond this and protects the assets from loss through theft, viruses, fire, technical defects etc.
A concept should be developed and strictly adhered to. The key word here is "Digital Asset Management". There are many contributions to this on the network that can be used as the basis for your own concept.

If I understand correctly, there isn’t any need to export anything, partly because Lightroom Classic can already work with images across multiple drives in a single catalog.

lauram69400745 wrote: “Can Lightroom calculate the 'original' size of the entire database so we'll know how much storage is needed to make an uncompressed backup?”

If all of the images you want to work with are already listed in the Lightroom Classic catalog, then the current file size of that catalog already represents how big it will be with exactly the same total images, stored on one drive rather than multiple. The Lightroom Classic catalog might even become smaller if you haven’t optimized it in a while.

If by “size of the entire database” you meant the space occupied by the actual image files and not the catalog (which is the actual database), there isn’t a built-in way to calculate that. You can make a list of all the top-level folders currently listed in the Library panel, switch to the desktop, have it tell you how much space each of those takes up, then add them up.

lauram69400745 wrote: “We're planning to select-all and then export-uncompressed. Is there a better way to create the archive?”

It’s unclear why it’s necessary to export uncompressed. It sounds more like you want all current originals to move to the single external drive. Assuming all of the images are currently listed in the same Lightroom Classic catalog, one way to achieve that is:

1. Plug in the external drive.
2. In the Library module in Lightroom Classic, choose Library > New Folder.
3. Using the standard file/folder dialog box that appears, go to the external drive and create a new folder that will become the top level folder on the external drive where you want to stopre all of the combined current photos. After you click Choose, that folder now appears in the Folders panel.
4. Staying in the Library module in Lightroom Classic, start dragging top-level folders from their current locations to the folder you just created on the external drive. This will move the actual files and subfolders.

If the images are currently listed across multiple Lightroom Classic catalogs, you can use File > Import from Another Catalog to merge them into a single master catalog.

We’re confused about what you mean by “export uncompressed” because it sounds like you want to decompress any compressed images (making them take up more space) and create exported copies that become disconnected from their current Lightroom edit history, collections, etc. Because those are all disadvantages, I’m guessing your intention is really to make sure all images are migrated without any loss of quality. The above steps will accomplish that.

lauram69400745 wrote: “Are there any things to avoid when choosing an external drive for this purpose?”

As long as it is a USB 3 hard drive, it should work fine. Because it’s going to be used for organizing and editing, avoid the cheapest types of drives that are marketed for backup because they’ll typically be slower. Try to pick up a hard drive intended for a professional workload, preferably 7200RPM. An SSD is even better, if the budget allows for the capacity you need.

The biggest thing to avoid: Storing the archive on one hard drive. If no backup plan currently exists, buy at least three of those drives and make sure the working drive is backed up identically to both of the others, with the backups updated on a regular schedule.

1. No, not if I understand your question. Take all the catalogs size, add em up, extrapolate but really, just get as big a drive as you can for all the images, catalogs (combined into one I assume) and FUTURE needs. 

2. So you can Export as Catalog with negs to the new drive. Now you'll end up with one master catalog (Import as Catalog from there?). 

3. Don't go too small! Drive space is cheap. If you currently have say 2TB of storage, easily considering doubling it; you'll be adding more images right? 

I'm not sure I understand what you are planning to do. First you say you plan to move all photos to a new drive. Then you say you are planning to export them and talk about a 'backup'. Are these two different things you want to do? Exporting does not move photos, it makes a copy. That means this is not the way to move the photos to a new single drive. Export can be used as backup, however. Depending on your settings, you can export as original or as tiff/jpeg. You can indeed use this to make a backup of your photos, but it's easier to just backup the drive with the photos on them.