"Saluta Publium nostrum amicissime et valetudinem tuam cura diligenter"
First of all,I hope you have already figured it out yourself,and being a novice in Latin myself,I would like to give my translation:"Greet to our Publius amicably and take good care of your well-being"this may seem a literal translation,but I think the idea is just expressed.
"saluta" and "cura" are just imperatives of "salutare" and "curare" respectively,as far as I understand them.
I am doing the reading matter these days,and now in the middle of Publius' story in Gaul. The story is interesting while I have to look up words from time to time in the Latin English Vocabulary,and not without parsing every sentence.
Fortunas tibi bonas