Which is a better lens combination for a Canon EOS 600D: 1) an 18-55mm lens plus a 55-250mm lens, 2) an 18-55mm lens plus  75-300mm lens  3) or a 18-135mm lens?

There is no "other" camera here apart from 600D! Well, let me introduce you something called 'body'. Canon EOS 600D is a body. There are many options, from 1200D till 1DX. And that numerals with an hyphen in between (as mentioned in your query)  are lenses. 18-55 is the kit lens. Usually people go for this. This is a general purpose lens. 55-250 is a telephoto lens (not super telephoto like 400mm or 600mm). 18-135 is a bit costlier (you must have noticed the price). This is because this lens is STM lens. Other two are not. Well, one more nifty-fifty lens is very common ( and available at a very low price). The 50mm f/1.8. Now, I will vote for 600D with dual lens kit. Though there is some inconvenience in removing the lens every time you need to, there can be good learning with different lenses.

Canon EOS 600D Canon EF-S 18-135mm f/3.5-5.6 IS Lens Canon EF 75-300mm f/4-5.6 IS USM Lens Canon 50mm EF f/1.8 II Lens will bw perfect Kit

It depends what type of photography you want to do.. If you love doing bird photography or want zoom telephoto lens then 55-250 mm lens is better than 75-300 .. As in later lens image stablization (IS) is not there... If you don't require zoom then go for 18-135 .. Performance of this kit lens is better than 18-55...

Both the 18-55mm lens and 18-135mm lens come in STM and are good lenses. I own the 18-55mm STM myself. If you can afford it, the 135 is nice. Don't choose the 55 unless you really really don't have $. (If neither are STM, ignore them and get other lenses) The 18-55mm + 75-300mm does make a good beginning combo, and I emphasise beginning here. None of them will survive an upgrade :) I would recommend, immediately get the 18-135mm, as your kit. As soon as you can, add a 50mm 1.8 for low light (they are cheap). Later on, get a big zoom or wide angle as you find out what you need.

Among the choices given, my pick would be #1, #3, #2, but it depends on where you're going with this. If all you'll ever want is some good pics of the kids, and don't see yourself doing anything more, just get the 18-135mm IS STM, and leave it at that. But, if you think you might want to make this a business, or are considering "going pro", start with a 50mm f/1.8 IS STM, and learn about it and yourself as much as you possibly can. Then after you've shot a few hundred to a few thousand pics, step back and think about what you shoot, and what you want to shoot. If you're always shooting flowers and bugs, get a good macro lens, such as the EF 50mm f/2.5. If you really like landscapes or architecture, consider either the EF-s 18-55mm IS STM, or the EF-s 10-22mm. If you're trying to shoot sports, but can't reach the shots you want, get the EF-s 55-250mm IS STM. I've tried to keep the lens in the good, but low budget range. I think everything but the 10-22 is only a couple hundred each. And that one is about 600, I believe. You can, of course, go to pro level glass at some point, but I expect that's beyond your range right now. Hope this answers your question. P.S. I do not consider any of the non-professional lenses of 70-300 or 75-300 length to even be worth looking at, except if you're in dire need.

I guess I got your question right :) 18-55 and 55-250 are the most sold combination with 600D. However, if you want to concentrate on wide angle photography, 18-135 is a great choice. Same goes with 70-300   if you want to click great macros or long range shots. If you have love for both but can't spend too much on the lens, you could go for the 18-55 and 55-250 as they could do the job at affordable rates. And also there are so many online offers with this lense combo. Hope I answered your query right :)

I have a 600D with the first combo but also a 50mm 1.8. So Telephoto, Zoom, Wide-Angle Landscapes and portraits alongwith Macro ( Have lens reversal ring for the Nifty fifty) are all the options I as a beginner can try my hands on. Whereas 18-135 is handy, will not provide satisfactory telephoto. Dont even go for a 75-300mm lens as it has on IS, as I believe you are talking about the lower model. and at 300mm, shake is prominent and will ruin your images if you dont have a tripod. 55-250 with IS is a pretty good deal there. People have complained about changing lens. If you have lack of eye-mind-hand coordination and have tiny hands then you would face problems. Otherwise not. I use 55-250 for wildlife and if I come by a nice landscape, It will take me just 1-2 mins max to switch lens, which is pretty neat as  am not photographing in high stakes where speedy movements and all are there. So three lens are a beginner kit serve a purpose for me and I hope will do the same for you.