Arabic learners hit this fork early, and the honest answer is "it depends on what you want to do."
What Modern Standard Arabic is
Modern Standard Arabic (MSA) is the formal, pan-Arab language of news, books, and officialdom. Nobody speaks it at home — it's the shared written and formal-spoken register across the Arab world.
What Lebanese Arabic is
Lebanese Arabic is the everyday spoken language of Lebanon and much of its diaspora — what people actually talk in, at home, with friends, in the street.
Diglossia, briefly
Arabic lives in two registers at once — a formal written one and a spoken dialect — which is why "learn Arabic" is really two related choices rather than one. Linguists call this diglossia; in practice it means you pick a starting point based on what you'll do most.
Which to learn for which goal
Reading, formal study, or working in writing across the Arab world → start with MSA. Talking with family, friends, or anyone in Lebanon → start with Lebanese. Many learners eventually want both — usually in that order of priority, driven by whether their goal is written/formal or spoken/personal.
Common questions
Can I understand the news if I learn Lebanese? Broadcast news is largely in MSA, so Lebanese alone won't fully cover it — though you'll catch a lot of interviews and everyday segments.
Will Lebanese work in other Arab countries? Partly. Lebanese is a Levantine dialect, so speakers of nearby dialects — Syrian, Palestinian, Jordanian — will largely understand you, and Levantine media has spread familiarity. Further afield (the Gulf, North Africa) it's less reliable, and MSA is the common bridge. So Lebanese travels well in the Levant and variably beyond.
Do I need to read the script to speak Lebanese? No — you can learn to speak Lebanese well before, or without, mastering the alphabet.