Every Minecraft server starts from the same place: Mojang's official, unmodified server jar. Whether it makes sense to move off that onto Paper depends almost entirely on how many players you expect and whether you want plugins.
What "vanilla" actually means here
Running "vanilla" means running the official server software exactly as Mojang ships it, no plugins, no extra configuration options beyond what server.properties already exposes, and gameplay that matches singleplayer exactly. It is also the only option with zero risk of ever behaving differently from what Mojang intended, since there is no fork-specific code in the mix at all.
Performance
This is Paper's entire reason for existing. The vanilla server is single-threaded for most of its critical work and was never built with large player counts or heavily explored worlds in mind. Paper's async chunk loading and generation, along with a long list of internal optimizations, let it hold a stable tick rate under loads that would visibly lag a vanilla server. For anything beyond a handful of players in a small area, this gap is not subtle.
Plugins and configuration
Vanilla has no plugin support at all, full stop. If you want anything beyond what server.properties and vanilla commands offer, economy systems, land claiming, custom commands, moderation tools, you need Paper (or another Bukkit-API server) to run plugins. Paper also exposes extra configuration Mojang's server does not, like tunable anti-xray and view-distance behavior per-world.
Where vanilla still wins
Vanilla is the only option with zero risk of plugin-caused bugs, since there is no plugin layer to introduce one. It is also marginally simpler to set up for a two-person world with no interest in plugins, and it is the reference implementation every fork is measured against for correctness. Some purist and speedrunning-adjacent communities specifically want vanilla for this reason.
Which should you choose?
For anything beyond a very small, plugin-free world, Paper is the better default: same core gameplay, meaningfully better performance, and the option to add plugins later even if you do not need them on day one. Stick with vanilla only if you specifically want zero non-Mojang code in the mix or you are certain you will never want a plugin.
Tick Hosting's panel supports both, with a one-click switch between vanilla and Paper (and everything in between) from the version selector, so you are never locked into your first choice. If you are unsure how much RAM either option needs for your player count, a RAM calculator can give you a specific number. Get started on Tick Hosting's plans page.