The default Ubuntu Desktop installation takes under 10 GB. Nowadays Ubuntu doesn't need a separate partition for swap, because uses swap file. It is good idea to have swap equal or bigger of the amount of you RAM. let's say you have 16 GB. Let's add 2 x 10 GB for further package installations, so at this point 50 GB looks pretty enough.
If you haven't used Linux/Ubuntu before, one new thing you must know is that the file system is organised in different way (such things as C:\ doesn't exist). There have one directory called root /, that represents the main partition and all other partitions could be mounted on a preferable location in the tree of root.
I think 250 GB should be okay for all user files. In Ubuntu, the user's home directories will be created as sub directories of the directory /home. On the private computers usually there is only one (main) user and its home directory will be /home/username. So based on my opinion, you need about 300 GB.
To do partitioning, during the installation process of Ubuntu, on the step Installation type you need to choose Something else. Then you will be able to create one partition with mount point / and one with mount point /home. Do not mount any Windows partition at this stage, they will be automatically mounted after the installation.
I would allocate 50 GB for / and 250 GB for /home. But you can choose a different scheme. Here are few premises that can help you with this decision:
Except the installation files, almost all other files will be saved in the user's home directory.
If you need extra space for media files, such these in Downloads, you can use the Windows (NTFS) partition(s) that you can access without problems from the Ubuntu side. The limitation is that NTFS doesn't support the Linux's permissions, but this is not a problem for the media files. For easy access, you will need to disable the fast boot option of Windows, which is not a big deal. Thus you will be able to share files between Ubuntu and Windows, easy.
Other huge things are the games. As I know you can play almost all Steam and Blizzard games on Ubuntu (under wine), so if you playing much games, maybe you will want to allocate more space (to /home). I'm a fan of StarCraftII and, on my poor i5-3rd generation laptop, it is much faster under wine rather than under Windows. But 2-3 games will spent about 50 GB.
If you work with some big raw media files (videos, photos), probably you will need more space, but the NTFS partition will serves well also in that case, I think.
If you plane to work with databases and some kind of services such as Apache, Nginx, Tomcat, etc., the directory /var will be important to you, and probably you will need to allocate more space to / or even you can create a separate partition for /var. For example an average MediaWoki installation is about 1.5 GB, the initial WordPress installation is about 50 MB, their databases will be 20-50 MB...
The last thing that comes to my mind is about the virtual machines - each of them will spent space at least as the minimal installation size of the guest OS.
After the creation of the partitions that you need for Ubuntu, you can leave the rest space as un allocated and create a new NTFS partition, later, under Windows. Or you can create this NTFS partition on the very same step and go forward.
Probably your Windows is installed in UEFI mode, so you will need to do some pre-installation setup - at least you need to disable the secure boot option from the BIOS. Within the comments already was provided an additional useful information according to that point.
I'm not going to disconnect the
windows 10 SSD drive C:\ (NTFS) either, because it seems like it might
be connected all the way in the innards of the laptop.
It is okay, Ubuntu will install its boot loader - GRUB - on the the boot partition an you will be able to chhose the OS you want to boot after the installation.
I will just install the second SSD into the other hard drive bay and I must be able to choose the correct drive in the Ubuntu installation phase. I'm a little worried about that, because how can I know which drive is which?
When you choose Something else ot the next step you will see two devices - most likely /dev/sda and /dev/sdb. The drive that contains your Windows will have 2 ot 3 partitions: one small EFI boot partition, one big partition with the Windows installation and perhaps one recovery partition. The other drive should be un-partitioned . So you will see something like:
/dev/sda
/dev/sda1
/dev/sda2
/dev/sda3
/dev/sdb
In that case your second device that you must partition is /dev/sdb and it must be partitioned.
I have a feeling that my windows 10 was pre-installed, and it is the UEFI mode thingy (I dont know what that means exactly though)
UEFI is just another type of interaction between software and hardware. As I know in this mode the OS can take control over the BIOS of some settings. The most important is that all OS must be installed in the same mode. So you must not disable EFI/UEFI from BIOS to install Ubuntu, just keep it enabled.
I don't understand why different guides tell to make swap partition for the Ubuntu and make also /var partition, and should I do that or simply make two partitions only, root partition for Ubuntu and /home partition for Ubuntu?
On Ubuntu 18.04, by default, the swap is a file located in you root partition, thus you can easily resize it without re-partitioning the drive. The previous versions of Ubuntu, by default, require a separate partition for swap.
You can use only one partition for your Ubuntu 18.04+ installation. The idea to have, as we say, /home and probably /var on separate partitions is that if you need to reinstall the OS, which usually requires format of the root partition, your user's data will stay untouched.
