You can certainly switch to another hosting plan at any time. LP has always permitted the unused balance of the old plan to be applied to the new plan, but I would check with sales just to be sure that's still the policy.
If you think you might soon outgrow the one database limit (or some other limit) on the Starter plan, consider beginning with the Basic plan. It's only a dollar more a month. Do be aware that "unlimited" resources still has limits -- your storage used has to be for the site only (e.g., no backing up your office PCs to your site), and you may hit the CPU usage limit at some point (and be asked to move up to a higher priced plan).
Email to email@example.com if you have specific questions that aren't answered here or on the sales pages.