I'd be fairly wary of the XFX R9 270, as despite it fitting into the requirements (they usually leave a little space anyway) I think the power connector is on the end of the card (rather than on the top, which is more common nowadays).
I can't be 100% sure of this as even XFX don't have good views of all six sides, but the image showing the top section doesn't appear to have a connector, meaning it's likely to be on the back.
This is a problem as it extends the effective length of the card by at least another 10mm or so (probably more once you allow for space for the cable to turn).
While I can't be 100% sure, it'd definitely be a concern for me, and I'd definitely look at cards with top mounted connector(s).
There will be cards that will fit. The GTX760 has a smallish PCB, so it enables a load of versions of it which are very short. The Zotac AMP! version, for example, has two fans and is very short, there is also the MSI GTX760 ITX, and Asus GTX760 Mini versions which are specifically for this type of scenario (though when the standard Asus DirectCU II version should fit too, you have to question the point of the "mini" versions a little). These are significantly more expensive than a basic R9 270, but it's perhaps worth consideration if you can't find a suitable card or don't want to step down to say a GTX750Ti.
As for heat/cooling, I doubt you'll have an issue. Nothing being discussed is going to generate vast amounts of heat, plus both sides are pretty well vented. Upgrading the rear fan is always an option if temperatures were a concern, as is upgrading the Intel stock cooler to something cheap but slightly larger like a Hyper 101/Hyper TX3 which will help to push heat from your CPU out of the rear of the case.
One final point is that the Lian Li isn't cheap (they never are). It looks nice, and is likely very well made, but if you are struggling for funds, then it's possibly a place to save. It's hard to beat something like a Coolermaster Elite 130 for value for money, and it'll fit any graphics card on the market, as well as a big PSU and an optical drive.