If you are in pandemic horde INC, you are 'non-gated'. This means you have access to a limited number of systems, but it's still 71. You just need one for ratting in though and just leave your vexor there. https://www.pandemic-horde.org/information/corporationbulletin/index has more details on gating.
If you are new to null sec ratting, please read the null sec ratting guide I made.
If you need fits for in horde: https://www.pandemic-horde.org/forum/index.php?threads/drone-lives-matter-a-drone-regions-ratting-guide-2-0.3340/
Perrigen Falls - Mostly ESI Gated https://i.imgur.com/qhdu3I5.png Colorblind: https://i.imgur.com/18C6gCa.png
The Kalevala Expanse - Mostly Non-gated https://i.imgur.com/yGbABrl.png Colorblind: https://i.imgur.com/3N2pzEZ.png
Geminate - Mostly ESI Gated https://i.imgur.com/8VFrj7O.png Colorblind: https://i.imgur.com/BggrTDJ.png
Etherium Reach - Half non-gated https://i.imgur.com/rr0Br5v.png Colorblind : https://i.imgur.com/ajmtAv4.png
Full map - https://i.imgur.com/sMTYFBY.png Colorblind:https://i.imgur.com/ajmtAv4.png
It goes Algos -> Vexor - > Ishtar -> PANKRAB (Marauder/dreads/supers)
There are other minor stop offs you can do, but most lead to heartache due to the Bigger isn't better philosophy.
Note that Gobbins redefined the maps recently: https://discordapp.com/channels/201704763874738176/385465973391622144/1312533548548362391
Also, no value, sr, decoy, navy, phx, mohist, probes (aka STAKAN UNIVERSE) etc are part of the extended panfam per this discord message, allowed to rat in our non-gated space. More specifically, Mohist Navy can rat in ESI-Gated space. Some like Tuda Suda Technology can run CRAB beacons in esi-gated space.
Note, the pocket we gave to Navy is fine to rat in for non-gated.