I would recommend you to buy a VPS server instead of a shared web hosting. Since there are a lot of limitations when it comes on shared web hosting. Limitations like executing files, bandwidth limit, lack of access, and there are more.
If you actually get a VPS Server, then there are no limitation except for bandwidth, storage and processing power.
You can get a quality uptime from these VPS hosting providers: FullTimeHosting, OVH, Hetzner Cloud, Vultr, DigitalOcean.
SSL: You can use a free ssl by letsencrypt (google it) or just use Cloudflare's free shared ssl by just adding your site into cloudflare and by changing your dns name server.
Budget: OVH starts $4.99, Hetzner Cloud starts 2.49 euro, Vultr starts $2.49, DigitalOcean starts $5, FullTimeHosting starts 3 euros.
Speed: Since its a VPS, its your own resources (resources like RAM/CPU/Network) and not shared.
If your not experienced enough, I would recommend you to buy a shared hosting since they have good support when it comes to web services.
Good Shared Hosting: FullTimeHosting, GoDaddy, HostGator, Hetzner Web Hosting