cPanel. Most hosts these days use cPanel. Its a user-friendly control panel that makes managing domains, email, and databases a breeze. Switching to another host later on is a snap if your old, and new host both use cPanel.
MySQL on localhost (Meaning, on the same physical server that your files are stored on). This will ensure snappy database access, critical to Drupal performance. (the exception to this rule is for some cloud-based services)
RAID 10. RAID 10 hard disk arrays offer the best in both performance and safety for your data.
Backups. Make sure your host performs regular backups so they can easily restore your accounts in case of a server failure. However, don't rely on those backups when you need to restore something that's your own fault. You'll need your own backups for that.
SSH access (Secure Shell). You may not need it now and you might not even know what it means, but someday you'll likely wish you had it. SSH access lets you handle many installation and maintenance tasks that you can't accomplish through other means.
Customer Support. Some hosts only offer email based support. Often, that's OK, but make sure you know what you're getting. If phone support is offered, pay attention to where it's based, if the hosting company discloses that much. Sometimes, overseas phone support is no better than domestic email support.