It is very rare for a customer to exceed normal usage while managing a website. Typically, customers only experience issues if they use their accounts for storage (for example large multimedia files) or file sharing. Our hosting services are not intended to support these activities, and in accordance with our Terms of Service your disk space and bandwidth usage must be integrated into the normal operation of a website. We offer various plans that better address high bandwidth and large storage requirements. Please contact us for details.
On the plus side, SiteGround offers free automatic daily backups, access to the Cloudflare CDN, high-performance SSDs for all plans, unlimited email accounts, and integration of the free LetsEncrypt SSL certificate into sites. The company does limit bandwidth and storage, but even those who claim to offer so-called unlimited bandwidth and storage really have some limits in their terms of service.
It's important to note, however, that not all shared hosting is created equal. Different companies use different servers, each configured with different amounts of resources, and with different features. Furthermore, some companies host more websites on a single server than its peers. As such, that $10 per month shared hosting plan probably has many benefits over one costing $0.99 per month.
Migration or transfer services are often free or offered at a reasonable fee. These services help move your existing site to the new hosting provider. They can save a huge amount of hassle. Just remember that the migration process is often automated, and may fit in with the host's processes and needs rather than yours. Not everything may migrate, and you may find the organization of the newly migrated site makes for harder maintenance in the long run.