My main concern with your current setup is that it's probably at or over its end of life expectation for the hardware, which can up and die at any moment. Then again, so can anything -- I've seen new laptops at work die after a few weeks.
My suggestion would be to make sure you back up any data you don't want to lose, think you *probably* don't want to lose, etc. You should be doing this anyway!
I'd do this on something like a high capacity thumb drive:
https://www.amazon.com/SanDisk-Cruzer-Glide-Drive-SDCZ60-128G-B35/dp/B007YX9OGW/ref=sr_1_3?crid=34LB72YYEOA8B&keywords=thumb+drive+128+gb&qid=1551454350&s=gateway&sprefix=thumb+drive%2Caps%2C205&sr=8-3You probably also want to go into your profile folder and copy things like your favorites folder and any other folders that contain stuff you want to retain. You can then dump these in your new user profile (if/when you get a new machine) to make your experience more seamless. I don't think Firefox is included in that, but I'd have to look and am not on a Windows PC right now.
W/ Firefox, if you make an account and sign in, it should follow you to the new machine whenever you sign in as far as settings/favorites.
The laptop you are considering is very nice. But I'll be honest that it sounds like much more than you need. You could achieve a good result for $300 (or less!). You also might consider a business class refurbished model, as they tend to be a little more robust than consumer grade.
Your old one has a number pad to the right on the keyboard, which you are likely used to using. In my experience, going from one of those to a keyboard without a keypad to the right is a pain. That might be a consideration.
You could also do what I typically do and use a program which backs up your current hard drive and dumps it all on your new one, but they can sometimes be finicky. For most instances I'd recommend simply transferring the truly desired data.
You mention slowness -- have you deleted temp files and such?
Windows 7 standard service support (updates and such) ended in 2015. Extended support ends in Jan 2020. Here's an article on the difference:
http://home.bt.com/tech-gadgets/computing/what-is-the-difference-between-windows-mainstream-support-and-extended-support-11364050710601I'd suspect you are currently running an unsupported version, which is a security concern.
If you aren't familiar with Win10, or don't want to be familiar with it (understandable), you could always go a Linux route w/ a desktop environment that is more in line w/ Win7. Examples include Linux Mint Cinnamon or MATE, or Ubuntu MATE.
If that sounds interesting to you, you could transfer needed data to your new machine, install Linux on your old machine to try it out, and then once satisfied w/ it simply do the same on your new machine.
Or, you could cuss and hit the new one until you get used to Win10
