I can't help you with the solar end of things; but, I might be able to help you figure out what size battery would work best for you and that is a good starting place.
You need to list every DC thing that you will be using your battery for. Write down what it is and how long you think you will use it each day. Look at each of these DC lights/fans/DVDs etc. and write down the Amperage (Amps) that each says it uses per hour. From that, you'll be able to calculate how many Amps you can expect to be using per day. Multiply that times 3 and then multiply that times the number of days you will usually be "off grid" and between chargings. That will tell you what size battery you will need. Once you get your solar charger set up, the number of days between recharges may need to be modified; but, keep in mind that, depending on the amount of available sun, your solar unit and its size and your Amp usage, you might be only supplementing and not fully recharging.
The reason for multiplying your expected Amp usage by 3 is that anytime you use more than 50% of your battery's Amp capacity, you shorten the battery's life. The current belief is that using no more than one third of the battery capacity will help give you maximum life from it.
Although a bit more complex that you need, you may be able to glean what you need from my calculation sheet and make a simpler one:
As far as what battery to use, I went with an
MK AGM battery.
...Maybe someone else can chime in with information related to solar and some other information.