What do you think is the best Linux system for older laptops with 4GB RAM, an old I3 and only one igpu?
Debian + Xfce
An i3 and 4GB RAM is more than enough for every Linux distro and Windows version.
I recommend Linux Mint Xfce Edition. It runs extremely fast on such old systems. Here is the download: http://mirrors.evowise.com/linuxmint/stable/20/linuxmint-20-xfce-64bit.iso In addition, Linux Mint is one of the most used distros.
Then write the ISO with Rufus https://rufus.ie/ on an empty formatted USB stick.
Simply boot the created stick and follow the instructions of the assistant. It offers the possibility to delete everything. Simply select "Erase hard drive and install Linux Mint" during installation. I recommend a full installation. The wizard will also set up the WLAN right away by having a network key ready. The latest Firefox is also installed at the same time.
This is what the desktop looks like
Manjaro is good
Lubuntu.
There are more economical, but "normal" old computers pack Lubuntu (& Lubuntu offers everything that a "clever" desktop system has to offer - you don't have one with minimally configured window managers & you have to install everything yourself, as it does with more economical ones Distros is the case).
I'm assuming you mean a really old i3 (1st Gen for example), otherwise it also packs a normal distro.
