I admit I don't know how you'd make browser goto ONLY https sites, but the suggestion
is recommended and definitely a good start.
I would also recommend "noscript" addon (firefox), but it does need tuning for each site. I'm guessing there would be a limited num of sites?
Possibly also "uBlock Origin".
In fact there are a number of security addons available, but you would need to read up on them.

Possibly you could describe a bit more exactly what this system is for and where you are getting the (security) requirements from - that could help us advise you better.
You may even want to look at the Security forum here at LQ

This project (setting up a machine that can do little other than browsing https pages) was put on hold for a couple months while we upgraded the internet service in our office. I wanted to see what options were available with the hardware that came with the new service. It can't do everything we need it to do, so I'm trying to pick up this project again.

Today I got as far as installing Ubuntu 16.04 (LTS) from a "Mini" iso. During the installation, I was prompted to select which packages to install. Those packages and others they depended on were then retrieved from the internet, I believe.

I told the installer two things:
1) *not* to install standard system utilities (this option was checked by default; I unchecked it)
2) to install "Ubuntu desktop"

For the first choice, my thinking was that I really don't want stuff loaded on without my knowing what it is, and that I could always install whatever I needed later by hand.

For the second, my thinking was that we'd need a desktop environment of some sort, and I might as well pick one.

After booting up after the installation, I was disappointed with what I saw. Firefox had been installed. Some kind of office suite (LibreOffice, probably) had been installed. A button with the Amazon logo was on my desktop. (Where did that come from?) So I guess choosing "Ubuntu desktop" installs a whole lot of stuff, not just a window manager and desktop environment.

I'd like to try again, and this time during the installation, I won't check any boxes for software to install. I'll investigate the option to add packages manually during installation, and if that doesn't work, I'll just apt them in afterwards.

What, at a minimum, should I tell apt to install if I want the Ubuntu desktop environment and nothing else? For instance, must I tell apt to install a window manager in addition to the desktop manager, or will the dependencies sort it all out automatically?

Thanks in advance,
Jim