3w led at 12v would yield a draw of .25 amps. with 10 of them that's 2.5 amps for 1 hour and makes it 2.5ah. for 5 hours that 12.5ah. battery capacity should never go being discharged beyond 50% so battery capacity will be at least 2x the ah calculated or 25ah. if you want to have a reserve for 3 days of use during less than sunny times then the ah capacity for one day will be x3 or 75ah.
to charge a battery you must know its ability in charging, but if you don't know then you can follow the generic range of 5-13% of capacity for the charge rate. 5% represents the slowest charge rate and the minimum i'd recommend you to use as this is a 20 hour rate. this equates to .05x75=3.75 amps needed from a pv. when dealing with solar you may find this can extend into a few days to fully charge the battery, especially if it is cloudy or rainy. also, don't forget that in the winter you may not get as many hours of fully rated sunshine too thus further extending the time needed to charge. at the 10% rate this is twice the current and twice as fast to charge your battery for 7.5 amps needed.
the more common batteries, and thus cheaper, are around 100ah and must be deep cycle as starting batteries will not last long in this use of them. if you go with a 100ah battery you can then calculate your needs for it.
keep in mind stc wattage ratings on pvs are maximum figures and are figures typically used to sell the pvs. those figures are not typically encountered in realworld use. the ptc ratings are better or even cec ratings.(california energy commision) generally about 10% more is needed if going by stc ratings. i concentrate on the current a pv is able to deliver for a given 12v pv. these will have vmps of between 17 and 17.6 volts typically. that means you need at least a 3.75a x 17v = 64w x 1.1 = 70.4w of pv minimumly.
rambling on here cause it's late so i'll conclude that most any pwm controller that will handle the current you'll maximumly need to deliver from the pvs (round up for common availabilities in controllers) that can accomodate a battery temperature sensor to handle charge voltage adjusts for fluctuations of temperature the battery will encounter.
a good example of a possible solution for you may be something like a kyocera kc85 to a kc130 pv into a xantrex c40 charge controller be it new or used, as there are so many out there and cheap, or go with something like the morningstar prostar 15 as it's new and cheap too. another good pv to use could be the evergreens that
www.sunelec.com has cheaply too. they sell seconds there as well for a cheaper price tag. don't forget the battery temperature sensor for the controller and the battery can be most any deep cycle out there with the proper ah ratings and can be had for roughly $100 or more. i can't be specific on pricing as battery prices are rising quickly. mounts for the pvs, wires, switches, fuses, etc. will all be needed too.