Start with the phrases that are heaviest in reward yet lightest on the tongue: SubhanAllah, Alhamdulillah, La ilaha illa Allah, and Allahu Akbar, plus 'SubhanAllah wa bihamdihi, SubhanAllah al-'Azim,' which the Prophet described as two words beloved to the Most Merciful. Also learn 'Astaghfirullah' (I seek Allah's forgiveness) and the short adhkar after prayer. These require no Arabic literacy to say and can be repeated throughout your day while you gradually learn more. Consistency in a little dhikr is better than a large amount abandoned.
Evidence — the daleel
On deen2u
Informational, not a personal fatwa. Consult a qualified scholar for rulings on your situation.