Laptop speeds have improved and cost has come down over the last 10 years. There is not much difference in price anymore.
PC Costs have gone down as well.
Your laptop battery will start out working great but will fade over time as 6'5'' pointed out. They do sell generic batteries for laptops under $50 to fix those problems
One thing I know is that people that are use to using a mouse usually hate the touchpad. You can always plug a mouse, keyboard or any other peripheral in to a lap top but that also means that you may have to transport those items if you intend to use your computer for a long period remotely.
On the other hand if you skype or facetime or facebook messenger video people, having a laptop is nice because of the built in camera. This technology is only getting better so if it is something that you want or plan to do, then the laptop is easier but you can always buy a peripheral (Camera) and plug it in to your desktop.
It pains me but I usually go the Scrappy route and buy refurbs. I have not had a problem with any of the refurbished computers I've purchased and I get them a helluva lot cheaper than retail. I have found that people either only buy refurbs or only buy new. There are not many middle ground computer buyers out there and even though I was able to convince one MadJacker to purchase a refurb there are even more people that I have failed to convince. I've decided to stop trying and just say - here's the cost difference which is roughly $500
Computer buying - These are the specs I look for
I'm a fan of the quad core Intel I7 Processors.
I look for a minimum of 8 Gbs of Ram
Hard Disk Space - I get 1 TB min - Go to your old pc - click start - click this pc - look below local disk C: and that will tell you how much space you have currently used on your computer. Storage is cheap so even if you double the amount you have used, you'll be in good shape.
In April I was able to get an I5 (Above Average), 12gb Ram, 2 TB refurb Lenovo for under $300 - from amazon
https://www.amazon.com/gp/product/B073GVZTSQ/ref=oh_aui_detailpage_o00_s00?ie=UTF8&psc=1
I'm running that as our office server and we've had no problems. I was not concerned about graphics or the fact it did not have hdmi since it was just a work computer but if it had been a home computer or even office computer I would have wanted hdmi and would have at least researched the graphics card
Desktop - Here's two Dell Refurbs that I wouldn't blink at purchasing
https://www.amazon.com/Dell-Inspiron-Computer-Certified-Refurbished/dp/B07DBT6MRQ/ref=sr_1_1?
s=electronics&ie=UTF8&qid=1528311829&sr=1-1&keywords=desktop+refurbished+hdmi+i7+8gb+1tb
https://www.amazon.com/Flagship-HP-...&keywords=desktop+refurbished+hdmi+i7+8gb+1tb
Better Graphic card and
not a refurb
https://www.amazon.com/Dell-XPS-892...11964&sr=1-5&keywords=desktop+hdmi+i7+8gb+1tb
Laptops 2 Refurbs
https://www.amazon.com/Dell-Latitud...1&keywords=laptop+hdmi+i7+8gb+1tb+refurbished
https://www.amazon.com/Dell-Dual-Co...3&keywords=laptop+hdmi+i7+8gb+1tb+refurbished
Not a refurb
https://www.amazon.com/Dell-Perform...4&sr=1-5&keywords=2018+dell+laptop+i7+8gb+1tb
Jack is correct - Carbonite is the way to go - One thing I like about Carbonite is I can be anywhere in the world and login and download a file that I need from the last 30 days. That is also the reason I haven't gotten big in to the Solid State Hard Drives that are all the rage right now. My Hard Drive can fail and all I have is a little head ache of fixing it because all of my data is backed up. For $70 a year it's worth it