I don't think anyone would argue that the Raven (caldari battleship) is by far the most efficient ship for solo level 4 missions (of course, improved versions of Raven, like Caldari Navy Raven and Golem are better, but they are just improved Ravens). There's no other battleship or battlecruiser that even comes close to the Raven for level 4 missions.
If you are strictly talking about level 4 missions, then go straight for the Raven. You can easily get the Drake along the way, since the skills cross over. Use the Drake for level 3 missions till you get skills/money for a Raven.
When you get your first Raven and start to solo level 4 missions: Save up all your initial ISK from the missions. Buy and completely fit a backup Raven at your mission headquarters. When you lose your first Raven, the backup will allow you to go back out and complete the mission then loot your own wreck. Never leave yourself in a situation where you don't have a backup mission ship prepared, no matter what level mission you are running. Everyone in Eve loses ships. Also, never forget to fully insure your mission-running ships.
The information on the following site will tell you all you ever wanted to know about missions, and more: http://eve-survival.org/
Most of the site even works on the in-game browser, maybe all of it.