Yeah it depends a lot on location. In more Northern climbs you're looking at shorter days with less sun so bigger batteries than those in built into lights. which then means out sourcing and upsizing the panel to cram energy in during those available hours.
My rough calculations (I'm not a professional nor expert so please consult one rather than relying on this as these could well be wrong or inaccurate) is (I could be writing out a Chinese food menu here for all I know!):
For just 30w of light on during the night:
30w for up to 16hrs a day in Winter = daily power requirement of 16 x 30 = 480w hrs? I'm ignoring the dusk to dawn swicth which would also add to the requirement.
The panel will need to be a minimum of 80w? therfore: - 480 / @ 6 hours of winter daylight on the shortest day = 80w to cram in those 480w hrs in just 6 hours (480/6).
There's a possibility of no or poor generation for days on end if dark or stormy days with no sun. Based on just 3 days of non generation (possibly not enough allowance), you potentially require 480 x 3 = 1.44kw / hrs ? of storage
Roughly - 100W panel = £100-250 depending on the brand ie not widely known brands or top brands
MPPT charge controller - @£100 (brand dependendent) although note the possibility of intelligent charging requirement for maximising lifespan especially for lithium.
Brackets, fixings etc - £100
For storage, 100 w hrs = 8.3 A hrs? (W=VA so A=W/V or 100/12 if 12 volt system = 8.33A).
So in this example we need @ 1.5kw ? storage = 15 x 100w hrs = 15 x 8.33 amps = 124.95 Ahrs so 125A hrs? of storage.
Batteries - 200A lead acid deep cycle @ £260 . A Lithium @ £650 Amazon or £1700 BattleBorn (well known quality brand)
If my maths and methology is correct, 200A should on the face of it clear it and give an extra few couple of days of no sun storage. Also some batteries don't like to go below 20% charge or above 80%, so you may need that factored in along with an intelligent controller that will; keep in those parameters, so usuable battery capacity may actually only be 60% of that stated (200AH x 60% = 120AH) so potentially under 3 days even at 200 ah. Obviously the next battery up or adding addditional batteries in parallel (consult expert before connecting differing sizes, types (almost definite no-no), or brands - I seem to remember they have to be the same size, brand , type and even charge matched before connection is possible - again ask an expert not me!!), adds a lot more cost.
However, even to run just 30W of lighting all night, is potentially costing at least around £700 upfront on lead acid and £2100 on Lithium by my hack up calulations, and that's assuming I've not missed or miscaluclated or under estimated anything and that's on the less than 3 day basis of not including chrage / discharge limits for liefespan maximisation.