With respect, I would strongly disagree with the above when it comes to video editing and gaming...specs are very important.
With all due respect. I meant back in the 1980s/1990s, it was very important to make sure you have the right computer specs for the software you want, because every new updated software kind of goes for the next new level of hardware. For example...
You have a PC with an Intel 286 processor and you have
Software v1 installed. (
Software could be anything. Microsoft Word, Corel
DRAW, etc. so let's just call it "Software")
When
Software v2 comes out, it request a PC with a 386 processor, so you have to be careful of making sure you must have the right machine specs.
When
Software v3 comes out, it request a 486 processor.
But nowadays, it seems that most software would say "Minimum system requirement: Intel 6th Generation" which means from Pentium Pro, Pentium II, Pentium III, onwards, including up to whatever new processor is on the market right now. Or it may say "Intel processor with 64-bit support" which could imply all of the Core models like i3, i5, i7, and i9 etc. Thus nowadays, any machines specs will do fine (as long as you have as much memory and a bigger HDD/SDD as you can afford). All that matters now is your budget, so pick whichever machine you like within your budget, and they will work fine with the software you want.
Forget specs, just focus on budget.
But YES, you are correct. Specs are important.
It is true that sometimes in some cases, specs is important specially when it comes to video editing and gaming. You're right, granted an i9 is faster than an i5, but it hardly matters because an i9, i7, i5, and i3, could work with the software if the software says "Minimum system: Intel processor with 64-bit support" so you could pick any one of them depending on your budget. And most important of all: You have to remember that how fast the machine is usually depends on the level of experience the user have. An experienced professional video editor could finish a project on an i5 before a rookie who only enjoy video editing in spare time on an i7. Your experience comes first, specs comes second.
The OP wants a laptop capable of editing photos and videos, while playing games in free time, but never mentions what type of games, for all we know, he means
Solitaire or
Minecraft and may not mean a hardcore gaming like
Call of Duty. The minimum requirements for photo and video editing software are likely to cover just about any laptops on the market today. Specs are a secondary option as long as the OP can pick any laptop on the market that needs to be above the minimum system requirement, apart from making sure that there is more memory and possibly a bigger hard drive, all within his budget. If specs was "very important" then the OP would be forced to a limited range of high end laptops and struggle with the budget and price tags.
Thus: Any laptops on the market will do fine as long as you includes more RAM and a higher HDD/SSD within your budget. Machine specs like i3, i5, i7, etc., hardly makes a difference because they all work with many software, and as long as you are patience with the video editing or gaming taking a while to progress the workflow.