As promised, this will be the first in a series of posts about solo L4 missioning. This post is written in the form of a series of tips for L4 missioners.
First and most obviously, get a battleship. The battleships that will be most effective at L4 missions are the Raven, Maelstrom, Dominix, Megathron, Armageddon, and Apocalypse. Take the Caldari sub-BS ships. You can do L4 missions in a Drake. You can do L4 missions in a Nighthawk. You can even do L4 missions in a Tengu. But sooner or later, you're going to want the DPS of a battleship platform. It really is the only way to do L4s quickly and effectively.
Forget about cap stability for L4 missions in a battleship platform. Being cap stable is over-rated, hugely expensive, and unnecessary. Damage in L4s comes in in waves and most battleships will have no problems managing the damage as long as you're smart about a) which missions you accept, and b) how you manage the aggro of the rats in that mission. More on that in a later post.
To solo L4s, you'll want a combined "gank plus tank" of around 1000 DPS. Any combination of the two will succeed, but gank is preferred and will allow you to complete missions much more rapidly. Gank is standard DPS taken from EFT, including drone damage. Tank is your peak recharge/repair rate for either shields or armor, also taken from EFT. For instance, a typical L4 mission Raven Navy Issue with a decent pilot aboard does 600 DPS, and has a peak shield repair rate of 700 DPS. This is a 1300 "gank plus tank" and this ship can therefore do L4 missions solo with no problems.
Get a faction battleship. While it is possible to solo L4s in standard Empire battleships, for most, it isn't easy and it isn't ideal. You will be much, much happier in one of the various faction battleships, which are tougher and quite often do much more damage. Some of the non-faction battleships are incapable of meeting the 1000 gank plus tank in the previous rule except with a highly skilled pilot aboard. Yes: faction battleships are expensive. Get used to the idea. If you fly it smart and fit it smart, you'll only need one. Faction battleships are actually usually more effective than Marauders and are just as cost effective, often even moreso.
Related to the previous two points, the more DPS you can bring to bear, the faster you will be able to complete a L4 mission, and therefore, the more ISK/hour you will make doing L4 missions. This is sometimes referred to as a "gank tank". In other words, you will kill the mission rats so quickly that they cannot bring their own DPS to bear on you.
With that in mind, plan on buying three to four navy faction weapon upgrades for the type of weapon that you will be using. These are Caldari Navy Ballistic Control Systems, Imperial Navy Heat Sinks, or Republic Fleet Gyrostabilizers, or the equivalent. Shield-tanking ships will have the advantage in DPS, and this is why shield-tanking ships are so preferred for running missions. In addition, plan on also buying faction weapons. You may not have to; for some faction battleships, T2 weapons are more effective than the equivalent faction weapons. But initially, plan on this added expense.
Keep telling yourself that over time, these expensive mods will be paying for themselves, hopefully many times over. ;-) The other good news is that these mods do not degrade in value over time (or at least, they haven't over the last three years). If you ever choose to sell your L4 mission ship, chances are excellent that you'll get every ISK you put into these mods back, if not even more ISK.
You will also almost certainly want to purchase a faction or dead-space repper for whatever type of tanking that you're doing. This is a Caldari Navy X-Large Shield Booster, Imperial Navy Large Armor Repairer, or (more likely for an armor-tanked ship) a C-Type or B-Type Large Armor Repairer. Faction and dead-space reppers are much more effective than their T2 counterparts. Over time and as you build up your DPS, you will not need these strong reps. But initially? They will be invaluable. And again, they retain their value well and can later be sold if you like.
Good faction battleships for L4 missions include the Raven Navy Issue, Tempest Fleet Issue, Scorpion Navy Issue, Apocalypse Navy Issue, Dominix Navy Issue, Rattlesnake, and Nightmare. Most of these are shield tanks because of the reasons above. However, the two laser boats have the advantage of being able to use inexpensive faction ammo. The Nightmare is particularly horrific in missions, because it is able to both shield tank and use faction laser crystals, and is therefore able to achieve or exceed 1000 DPS in gank alone!
Start with missions against pirate factions that emphasize your ship's strengths and their weaknesses. Don't be afraid to travel to regions that support these rats! For instance, the Raven is strongest against Sanshas and Angel rats thanks to its long-range weapons and versatile weapon damage. Sansha/Angel rat missions are most common in Minmatar and Ammatar space, so travel there!
Build up your faction standing so that -- over time -- you can do L4s throughout the galaxy. Initially, this will be the easiest in Amarr space. Doing Amarr missions builds up your faction standing with the Amarr, Caldari, Ammatar, and Khanid factions. Amarr space is the home of Blood Raider rats, which will be the easiest to kill in the Raven Navy Issue, Scorpion Navy Issue, and Tempest Fleet Issue and their non-faction counter-parts (including the Maelstrom).
Avoid accepting missions against the six Empire factions. Sooner or later, you're going to want to build up standing with these factions. It's much easier to do if you haven't spent weeks killing their ships at some point in the past.
Agent mission quality is (currently) very important. However, it is more important to have access to several agents in close proximity with relatively high quality rather than one agent with extremely high quality. If you only have a single agent and that agent offers you two poor missions in a row, your night's missioning is over. However, if you have two or three nearby agents with decent quality, you have many more chances to accept only good missions, declining poor ones.
Confine yourself to 0.8 and higher security status systems, 0.7 at the very lowest. Suicide gankers live for finding expensive faction battleships, particularly glass cannon faction battleships, in 0.5 and 0.6 systems. It doesn't take very many T1 battleships to take you out when you are heavily engaged in a L4 mission. Keep it in mind. By the same token, do not officer-fit your L4 mission battleship. Yes, I know it's popular among the set that has more ISK than brains. Don't be like them. Officer-fit battleships aren't even safe in 0.9 systems.
Don't risk your money-maker! Do not take your expensive faction-fit mission ship on any PvP op whatsoever. If a war-dec occurs, your money-maker stays docked and does not undock until the war is over. EVE lore is full of missioning and ratting ships getting killed because they were brought in on ops they had no business being brought in on.
Finally, get a second account! Completing L4 missions with two accounts is much easier than doing it with one. You will complete missions more than twice as quickly due to DPS stacking and earn more ISK overall this way. You can also use remote rep tactics, remote rep drones, and can choose two battleships with complementary damage and styles. For instance, a Maelstrom and a Raven work exceptionally well together. A mission-fit Maelstrom can do 10,000 HP or more volley damage, devastating rat battleships with a single salvo. The Raven then finishes that target off with cruise missiles while the Maelstrom's next volley goes against the next rat.
Hopefully, this guide has been helpful. In my next post on this subject, I'll talk about specific tactics once you have your battleship (or battleships) in a mission.