You can start with VPS and upgrade to dedicated once needed.
When you are looking for VPS provider make sure that it comes with:
- Enterprise SSD storage in RAID10 is used ( a must for large databases)
- High performance CPUs are used (XEON 3.0Gz+)
- Guaranteed 100Mbps bandwidth speed (or more)
- DDOS protection (nice to have)
- Semi or fully managed service
- High Privacy Protection standards ( you don't want your profiles leak around)
Don't be cheap (cheap VPS = downtime/overselling)
Consider using premium CDN if you are targeting multi-locations.
Good luck with your project