Looking at A2, I would stay away from them. They charge $3/month just for "cloudflare basic," which translates to CloudFlare's free package if you ever wanted to use them. I've never seen a hosting company charging for something like that.
Honestly, I would never use basic shared-hosting for a Laravel app. It's fine for things like Wordpress, but that's about it. One of the problems you get with a lot of shared hosts is them trying to "force" you into bigger packages. You get a traffic boom, the database gets hit hard and then suddenly your site is suspended for overuse of resources (HINT: nothing is unlimited despite what they say!). The only way you get your site back up is to upgrade to the next higher plan.
Something else that always gets people is manged -vs- unmanaged. Many thing manged means if there's a problem with your software, they will fix it. Nope. They will handle things related to the server going down, but that's pretty much it.
Going with what everyone else said, go with VPS. It will be a little more headache and learning to get setup, but you're also learning something new and in the long run will have much less headaches and save money.