The less expensive cleaners will be painfully slow in a pool that size and won't do a great job. Conversely, the higher end cleaners like the robots are perfect for your pool but they can be 4 times the cost.
I don't have a ton of experience in the pool arena but..I did buy a zodiac G4 last year it works off your skimmer. It takes a few minutes at first to hook up but once you have done it a couple of times I loved it! I would go out at night and set it up like once a week and wake up to a perfectly clean pool. I would however mention that this is a regular maintenence cleaner. I don't beleive it would work well if you have lots of issues with large debri or excessive leaves. Some will use the installable skimmers to help collect the leaves and I've heard that it helps although I do not have one of these. BTW mine cost about $525 last year not sure what the price is now.
Dave is kind of right. My G4 is slow that why I opted for night use. Since I didn't have to do it much it was worth it. Also with mine I did have to clean the filter after use, but I had a cartridge filter and just hosed it off with a high pressure nozzle and it worked fine. Not sure what you have. Might want to put the specs for your pool down below Unless you did and I missed it.
I have a Blue Diamond,and it does a really good job. My pool is 18*36, and is a gunite/plaster pool. The only place that the robot doesn't clean is the swim outs on the deep end corners, and the steps/bench on the shallow end. It does a good job on the water line, but some brushing will always be required.
The down side is that the filter bags can be a pain to clean when they get truly nasty. It generally takes me 5-10 minutes (on average) to clean the filter bag.
This is the first year that i have used this cleaner, so i can not comment on service life or long term cost.
Hope this helps.
There are a bunch of robots available and many of them are identical...just "private labeled" to confuse the issue. I even found a website that showed all the robots and which ones were the same but I lost it and couldn't find it again.
So, even within robots, the more you are willing to pay, the more cleaning power and speed you get. I think the "Blue pearl" is about 750-800 or so (I really am guessing) and that should provide enough cleaning power for a 20x40 pool.
My pool is large and my first cleaner was a "little shark" (suction) for about $300 or so. He simply couldn't do the job....too much pool and too little cleaning power. That's not a knock against "Sharkie".....I think I would've gotten similar results with any cleaner in that range.
I recently bit the bullet and bought a blue diamond R/C for $1350 (Yikes!! ) but, to this point, it has been worth it. It cleans my pool in about 1.5 hours and, best of all, does so without me running my pool pump for the 10-12 hours I had to do when "Sharkie" was doing the cleaning.
Of all the robots, I think Aquabot sells more than anyone and they make them in several price ranges. Dolphin robots are probably next in sales volume. I've seen posted on this forum a couple of comments that folks think their Dolphins were built a little flimsily.
Anyway, you'll have to research them and figure out what makes sense for you. I will reeemphasize that my learning experience came to the conclusion that you pay for cleaning power.
I have been looking at the Aquabot models, the T2 looks too be a good fit. I imagine I will be going with this model unless others advise against it or offer a suitable alternative in the same price range. The Blue Diamond looks great, but a little too pricey for what I am looking for.
I grew up in MIllburn (Essex Co.) and can remember when Short Hills was the neuva riche part of that town (which is why iit used to be called Millburn/Short Hills)! (MY family was from 'the Estates"--the Millburn part!)
(Gotta live or have lived in Jersey to understand!)