Which external GPU is the best/recommend for my laptop?

It's not an issue of the Intel CPU, but the fact that you got the wrong laptop for gaming, it's the video card that's the issue.

Do you have a mini PCIe slot in your laptop? Then you can get an external adapter, but it's limited to PCIe 1x speeds, will need a power supply sitting at your desk connected to the video card and will have a wire hanging out of your case, which will have to be modded or left cracked open to allow the external cable to run out of it. You also can't use that video card with the laptop screen, it has to be attached to a monitor.

If you are OK with all that, ebay has the external PCIe adapters you need, a 300 or so watt Corsair CX power supply is enough to power a video card, and a GTX 750 Ti card is OK, although it may be bottlenecked by the interface speed. Maybe a regular 750, or even a 740 may be OK to use.

External video cards are never really "recommended" for any laptop, the best reply is "sell the laptop, buy one with a good video card that will last for gaming for 3 years", meaning at least a mid-range one or higher.