-Operating System: Windows 8 64bit
-Model: Dell Inspiron 3721
-Intel Core i5
-Memory: 6144MB RAM
-Graphics: AMD Radeon HD 8730MB
Intel HD Graphics 4000 (this was under the "Display" in dxdiag)
Run it at the highest settings you can get away with and still maintain acceptable framerates in the game.
The AMD Radeon HD 8730M is a mid range, desktop replacement graphics chipset is should the run fine at the laptop's native resolution of 1600x900.
Since you have an integrated Intel HD graphics chipset also, you need to make sure the AMD Radeon is used while gaming. You should be able to force certain applications to use the AMD Radeon (High Performance) from within the AMD Vision Engine Control Center (Catalyst Control Center).
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I would set Skyrim to High (not Ultra), its a mid-range card (Class 2).
It depends on the particular ENB you're thinking of using and the settings you use, but a lot of them have a major performance cost. I'd be careful using them and read up on them thoroughly before using them.
Make sure you have both TESV.exe AND SkyrimLauncher.exe set to use the Radeon.