The best of the Gundam series are probably Zeta and Turn A. Zeta is a sequel to Mobile Suit Gundam so it requires that you watch MSG, 08th MS team, and 0083 first to get all of the backstory and a full picture of the political situations of the series.
Turn A is quite good but is very different than other gundams, much like G Gundam.
Really, the best way is to watch the UC timeline which goes MSG, 08th MS Team, Gundam 0080, gundam 0083, Zeta, Double Zeta, Char's Counterattack, Gundam Unicorn, Gundam F-91, Victory Gundam
There is the Cosmic Century timeline which is SEED and SEED destiny which suffers because SEED is a somewhat mediocre remake of MSG and Destiny is a pile of failed potential that gets increasingly stupider as it goes on.
One of the most interesting series is the Alternate Century tale Gundam X which is an altered history story but suffers because the series was condensed during the last chunk of the series so the ending feels exceedingly rushed.
G Gundam is a whole bunch of hilarious awesome that is totally ludicrous and over the top but displays very strong storytelling skills.
Gundam Wing is generally mediocre because it has much weaker main characters than the rest of the series but this makes it a pretty good introductory series because there is a lot less to keep track of.
