I've a pentium 4 heater on besides me. Spec wise I record it as
hp dx6120mt (mini-tower, pentium 4 dual core, 3gb, winfast clone of nvidia 7600gt)
which I only semi-recently upgraded the RAM from 1.5 to 3gb. I have no idea what speed it is, I only record CPU, ram & GPU.
I'm using it for QA-testing (QA=Quality Assurance) Lubuntu 18.04.4 which is due for release on Thursday (6-Feb-2020; thus I'm somewhat busy & may not have noticed your prior reply). It's one of my test rigs that tested up to Lubuntu 19.04 (it's x86 only now; and this 18.04.4 release will likely be it's last use for QA-installs).
I can't speak to the various pentium 4's; I used to have a couple but kept this one as it used SATA & PATA drives.
Yes the alternate installer is very different; it uses the 'debian-installer' instead of Ubuntu's standard `ubiquity` installer; it's used to save RAM. The debian-installer was primarily used for installing on servers (which are text-mode only often), though may not be used for any 20.04 release. The new 18.04.4 images do not include any 'di' or alternate images; alternate images aren't updated.
I have tested using many pentium M (2003-2005) laptops, and a few pentium 4 boxes (now only 1), but I haven't done any testing on any box with less than 1GB of ram in a long time. Thus your situation in regards RAM I cannot advise on. I'd be tempted to use something like 'openbox' or a simple window manager; though I realize this won't likely mean much to you.
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