Hi Matthew! The more narrowly you pose your questions or issues, the better focused we can be in our responses. We now know more about your situation, and I certainly don't envy the high cost of bandwidth you are paying. A typical modern Linux distro runs about 1.2 GB that you burn to a DVD or USB. That would cost you $12, but if you got a bad download and had to do it again it would be even worse. (It happens... check MD5 or SHA256 checksums after downloading to verify integrity.)
There is a link at the top of this site's pages to
OSDisc.com where you can buy most Linux DVD's for $5.95 each ($9.95 on 16GB USB flash drive)... if you purchase $20 or more you can also get free worldwide shipping (since we don't know where you are either). Look for those described as "Install/Live" in most cases. You need to know whether your laptop and desktop are 32-bit or 64-bit.... I mean the CPU, not whether Windows is 32- or 64-bit. You don't want 32-bit unless you must use it (for reasons too long to write out just now). So if you buy 4 DVD's for about $24, you will get free shipping and have something to work with. Another alternative might be to use a library or wireless hot spot somewhere near you to download for free, if you haven't already considered that.
But we still still don't know nearly enough to give you the best advice. You don't say if WiFi is necessary in your home network. One very important bit is how much RAM on the laptop and the desktop that you plan to use? Any distro that you consider will publish their
minimum system requirements, but if you are scraping the bottom of those requirements you may still be disappointed with its performance. Though you have past experience, you are still a relative newbie with today's Linux... therefore I would not recommend that you return to Slackware. (I don't know about shadow passwords offhand... that is really not an issue for you at this time.)
You seem to want us to pick for you, so I will name 4 distros that I would choose at this moment (not knowing your RAM, etc, but expecting you to check minimum system requirements). Someone else may give you 4 different picks. It will still fall to you to do some homework and make your decisions, and it will not be our fault if you have hardware compatibility issues. We don't know everything (not even on a good day), and we basically still know
nothing about your personal hardware!
1. Linux Lite 3.4 (supported until April 2021)
2. Linux Mint 18.2 (MATE Edition, also supported until April 2021)
3. PCLinuxOS 2017.07 (MATE Edition, 32-bit not available, "rolling release" so always updated to current)
4. openSUSE Leap 42.3 (32-bit not available, supported through January 2019, much less than others listed)
Reasons:
1. & 2. Linux Lite and Mint are both based on Ubuntu. They provide some of the best hardware support, especially WiFi. I feel the MATE desktop in Mint is better for lower-end video cards or onboard video. Lite uses a modified XFCE desktop which is also very resource friendly. I usually use one of these on my own desktops and laptops, so of course I highly favor them and recommend them.
3. PCLinuxOS is independently developed. So if there is an "Ubuntu-specific" hardware compatibility problem, there is a chance that PCLOS will not have that same problem. The MATE Edition is much more resource friendly than the KDE alternative they offer.
4. openSUSE Leap is also independent from other developers, and Leap is the Stable Edition. Many desktops can be picked during installation... pick "Custom" and then choose LXDE. The LXDE desktop is the most resource friendly, even better than MATE.
Alternatives:
1. Ubuntu version 16.04.3 (note this is
NOT the newest Ubuntu, but it has the longest support until April 2021)
2. LXLE (Ubuntu-based using LXDE desktop... be sure to get long term support version)
3. Lubuntu (This actually is Ubuntu, but with the LXDE desktop... be sure to get long term support version)
Above, you said, "I will need video along with telecommand and telemetry." but I am not really sure what you mean by this. What kind of video? I've typed enough for this round anyway, and you can describe these more next time.
Cheers