CPU: The more recent, the better. Intel still has stronger single-threaded performance than AMD at any price, as far as Dolphin is concerned. I can't comment on AMD's most recent message mobile CPUs, but generally you can't go wrong with mid-range Intel mobile CPUs for bang/buck performance. Dolphin typically will use two cores/threads for the bulk of its workload. If you give it more, that helps with any background processing. An i5 (4 cores/4 threads) is a nice balance. An i7 is overkill, and hyperthreading isn't all that great anyway from what I hear.
With this price range, however, you're generally stuck with an i3. The i5 you mentioned (i5-8250) has a low base clock. Remember, once you start doing something intensive, the CPU's workload increases, it generates more heat, and it will potentially scale back the clock to help cool it off. I always assume that's going to be the case when you're running Dolphin (I mean, you can't guarantee that won't be the case). A higher base clock means you won't drop below that threshold, which is guaranteed performance. With a lower base clock, it's a crapshoot basically, and it all depends on how cool you can keep your machine. So, be wary when looking at those "boosts up to 2.7GHz with Turbo Boost" since those are all dependent on specific thermal conditions.
Everything else is up to your preference. Dolphin happily runs on 4GB (the de facto minimum these days). 8GB is fine, but more than you'll ever need for normal Dolphin gameplay, unless you plan to be doing memory intensive stuff while playing Dolphin (compressing files, encrypting files, editing video), but realistically you really ought to be playing Dolphin and doing not much else besides Discord maybe. SSD or HDD is your choice; doesn't make a difference to Dolphin. Bluetooth is a nice bonus because you can use a real Wiimote with Dolphin.
All of these mobile Intel CPUs (at least the ones from the laptops posted above) tend to run the Intel HD620. Not much options there. PC gamers scoff at integrated GPUs because they're generally inadequate for most new games on anything other than low/medium quality settings, and even then likely not 60FPS. But Dolphin's GPU requirements are vastly lower. As I said, with the Intel HD620, you can get fullspeed using 1x resolution in many games (480p effectively) and some of the lighter games run fine at 2x (720p effectively). Going to higher resolutions will cause slowdowns, but most games are playable with low resolutions. Again, getting a dedicated mobile GPU ups the price, but it would allow for higher resolutions. Sub $500 laptops don't offer dedicated mobile GPUs unfortunately.
About the laptop you linked to above, I'd avoid the i5-8250U for the reasons stated above about low base clocks. 1.6GHz will struggle with Dolphin. The 16+ GB optional RAM sounds like something you can choose during check-out, but at an added price. The integrated GPU is the HD620. I'd find something else. As I said yesterday, if it were me, it's really a toss up between something with an i3-7130U or i3-8130U.
With this price range, however, you're generally stuck with an i3. The i5 you mentioned (i5-8250) has a low base clock. Remember, once you start doing something intensive, the CPU's workload increases, it generates more heat, and it will potentially scale back the clock to help cool it off. I always assume that's going to be the case when you're running Dolphin (I mean, you can't guarantee that won't be the case). A higher base clock means you won't drop below that threshold, which is guaranteed performance. With a lower base clock, it's a crapshoot basically, and it all depends on how cool you can keep your machine. So, be wary when looking at those "boosts up to 2.7GHz with Turbo Boost" since those are all dependent on specific thermal conditions.
Everything else is up to your preference. Dolphin happily runs on 4GB (the de facto minimum these days). 8GB is fine, but more than you'll ever need for normal Dolphin gameplay, unless you plan to be doing memory intensive stuff while playing Dolphin (compressing files, encrypting files, editing video), but realistically you really ought to be playing Dolphin and doing not much else besides Discord maybe. SSD or HDD is your choice; doesn't make a difference to Dolphin. Bluetooth is a nice bonus because you can use a real Wiimote with Dolphin.
All of these mobile Intel CPUs (at least the ones from the laptops posted above) tend to run the Intel HD620. Not much options there. PC gamers scoff at integrated GPUs because they're generally inadequate for most new games on anything other than low/medium quality settings, and even then likely not 60FPS. But Dolphin's GPU requirements are vastly lower. As I said, with the Intel HD620, you can get fullspeed using 1x resolution in many games (480p effectively) and some of the lighter games run fine at 2x (720p effectively). Going to higher resolutions will cause slowdowns, but most games are playable with low resolutions. Again, getting a dedicated mobile GPU ups the price, but it would allow for higher resolutions. Sub $500 laptops don't offer dedicated mobile GPUs unfortunately.
About the laptop you linked to above, I'd avoid the i5-8250U for the reasons stated above about low base clocks. 1.6GHz will struggle with Dolphin. The 16+ GB optional RAM sounds like something you can choose during check-out, but at an added price. The integrated GPU is the HD620. I'd find something else. As I said yesterday, if it were me, it's really a toss up between something with an i3-7130U or i3-8130U.