In my case of not wanting batteries for the particular setup mentioned, it would be to cut out the high cost & the space required for them. Obviously if such a setup is even possible, I'd need a good voltage regulator of some sort. partly-cloudy days where the sun is constantly in & out of the clouds might be an issue, if there's allot of stitching between solar/grid I don't see a problem, but say the lights were solar only & I couldn't use grid as a backup.. for plants I don't see constant on/off being too much an issue, but that wouldn't be good for fish!
The lights that would be powered are all fluorescent (only change that might need to happen would be to upgrade the smaller ones from magnetic to electronic ballasts)
All essential loads such as fridge/freezer/furnace/etc would be left as-is on more reliable grid power. (the idea really would be to not have the solar integrated into the house's electrical system)
Even if its do-able, I'm not sure there would be enough roof-space for however many panels would be needed? Quite a few I'm assuming/have no idea how much can be run off a panel. Still might be totally impractical even if 'it can be done'?

The 2nd part I mentioned of an off-grid cabin, that would obviously need batteries since one of the main ideas there would be to have light at night. Which I agree with Roi_hartmann, LED would be the way to go.
Other than that only loads I could see would little things be for charging phone/computer & some sorta small stereo system (don't need blasting music .lol. or a TV)
(something like this would would be used for weekend getaways mainly in spring/summer/fall .. so only a small fridge would be needed. no other appliances like clothes-washer since that could be done at home)

Personally, I can't think of a better use than my oily lampses, heat and warmth. 

I agree with Sammi's idea

4. LiFePO4 batteries should last 8,000 cycles. But what's actually such a cycle (in a day with changing weather, part of the time charging, part of the time discharging...)
5. An older site suggested truck batteries as a cheaper starter.

Lead acid (truck batteries) has been a mature and proven tech for a century. They don't randomly burst into flames. They easily last over a decade if treated properly. They're cheaper and can be sold for scrap for a reasonably sum at EOL, at which point they can be fully recycled into new lead acid batteries with minimum environmental impact. I'm still not sold on lithium for a stationary application where weight is irrelevant.

Truck batteries are exactly what kind of batteries you wouldn't use in cyclic use: they are designed to deliver peak power, not continuous power: they won't provide the energy you want and won't last much more than a bunch of years.
Proper lead acid batteries for off grid living exists, but they are very different in construction and they cost much more.
If you read lead acid batteries datasheet, you will notice that they can deliver a lot of cycles if discharged much less than lithium batteries and yes, they can burst in flames too if stored in wrong places: during charge, they split water into H2 and O2, this is why they must reside in a well ventilated area and must be refilled with distilled water.

I like the ideas and creative thoughts here!

As for batteries, deep cycle lead acid should be sufficient (typical automotive batteries aren't deep cycle rated.) They are less expensive and somewhat safer than lithium batteries. I maintained a set of GC2 batteries (golf car batteries) in our scissor lift at work, and they lasted 9 years. Just check the battery acid level periodically and add only distilled water.
Or you could use deep cycle sealed lead acid batteries, then you won't need to water them. SLA batteries are often used in deep cycling applications, such as battery backups and emergency lighting. Typical life expectancy in those applications is 5-7 years.

Yeah, for a stationary application I'd say deep cycle lead acid like what you seen in a large marine battery is still a good choice. Automotive and truck batteries aren't designed for the type of drain that powering a off grid system has, they're only really designed to provide a brief high current draw to run the engine starter.

SLA is a option too but I'd imagine those would be more expensive compared to the marine deep cycle batteries.

For the fridge, if you plan to have a fuel supply such as propane for heating, you could also choose to get a propane refrigerator instead of conventional electric one. 

The propane fridge is a really interesting idea! My grandparents had one where coal gas expansion did the work. I'm just not sure if this kind of refrigerators is still available and how much propane they consume. (The expanded gas could be used for heating water - in case of my grandparents it was just heating the room - not the best thing in summer...)

Yes sorry I should have made that more clear. Deep cycle type not "starter" batteries. Poor choice of terminology on my part! Starter batteries with their thin plates obviously won't last in a solar application.

Sealed are typically a lot more expensive with shorter lifespan, although their lower internal resistance does allow faster recharging and better handling of current peaks (eg. induction motor starting) where the battery size is marginal. I feel vented lead acid is the best value. Just make sure it's adequately sized.

The risk of hydrogen gas explosion is easily managed with proper ventilation