Gundam 00 1st and 2nd season are where I would go from that point, great story as well has a good focus on some of the civilians view points on everything happening in a Gundam series. If you can find the movie watch that.
If you never watched Gundam Wing or G Gundam those can be fun more nostalgic series, also has some cool suits. Just don't question stuff from G Gundam like the Tequila Gundam.
As for main Universal Century timeline I would recommend watching the compilation films from Mobile Suit Gundam, then for UC series Zeta Gundam, ZZ Gundam, and the OVA Char's counter attack. That will get you the basic primer on knowing what is happening in UC Gundam, from there you can move into Mobile Suit Gundam Unicorn, either the OVA or re-cut of it which can be found on the Gundaminfo Youtube channel. That gets you caught up to right before Mobile Suit Gundam NT which releases in the US tomorrow, 2-19-19 if you are reading this later.
I personally recommend two other UC OVA's which as Mobile Suit Gundam 8th MS Team, and Mobile Suit Gundam Thunderbolt, Thunderbolt is on the Gundaminfo Youtube channel as well in the form of the compilation films. Both of these OVA's take place during the One Year War which is the setting of the original Mobile Suit Gundam, so you can either watch them after that or anytime after.
That is my basic list of which Gundam series, movies, and OVA's I recommend to those getting into the franchise.
Some series can be interesting to watch later on like Gundam Age as it has a short trilogy lay out story following one family and their efforts using Gundams, Gundam Build Fighters and its accompanying series are fun to see new takes on older suits, but not crucial to watch.
TLDR: Move to Gundam 00 as it is another self contained universe within Gundam. Watch Wing or G Gundam if you find the suit designs interesting. Watch the main four series from the UC timeline, then Unicorn before going to anything else UC. Many of the OVA's take place during or shortly after the One Year War so that makes Mobile Suit Gundam crucial to watch first regarding UC.