As a new beginner of Swedish, should I learn some daily speaking first or the grammer first?

It is better to learn basic grammar first, then simple everyday sentences. Have a look on the net for free audio tapes in Swedish.

Hello Crystal,

You should start by taking some initial courses where you get introduced to the language and learn simultaneously ( at the same time) basic wording, basic grammar and pronunciation .Your tutor could combine them all in a lesson.
Good luck:)