re: Need a new desktop

Yeah, you could build a good one for that budget, but the issue is whether you really need a $1,000 PC for basic home use, even keeping in mind the fact that you want it to last a long time.
Speaking of longevity, go ahead and stop looking at all-in-ones. They are basically big-screen laptops without a battery.

Home/Office PCs aren't inherently better when custom-built, but you can certainly make them better (meaning, a lot of those basic $500 i5/8GB/1TB HDD desktops are not much cheaper as a DIY build, and you don't get tangibly higher-quality parts if saving money is the primary goal).

That said, you've already demonstrated an ability to follow directions, and having even the slightest interest in learning to build one yourself is a good enough reason to do it.

Here's a part list using just Newegg and Amazon inventory:

PCPartPicker part list: LINK
Price breakdown by merchant: LINK /

CPU: Intel Core i5-6500 3.2GHz Quad-Core Processor ($199.99 @ Amazon)
CPU Cooler: Cooler Master Hyper 212 EVO 82.9 CFM Sleeve Bearing CPU Cooler ($24.99 @ Newegg)
Motherboard: ASRock H170 Pro4S ATX LGA1151 Motherboard ($94.99 @ Newegg)
Memory: Crucial 8GB (2 x 4GB) DDR4-2133 Memory ($39.99 @ Newegg)
Storage: Samsung 850 EVO-Series 250GB 2.5" Solid State Drive ($89.99 @ Amazon)
Storage: Western Digital Caviar Blue 1TB 3.5" 7200RPM Internal Hard Drive ($54.99 @ Newegg)
Case: Corsair 330R Blackout ATX Mid Tower Case ($69.99 @ Newegg)
Power Supply: Corsair CX 500W 80+ Bronze Certified Semi-Modular ATX Power Supply ($34.99 @ Newegg)
Operating System: Microsoft Windows 10 Home OEM (64-bit) ($96.00 @ Amazon)
Total: $705.92

This is essentially a gaming PC configuration minus the graphics card. This build could be scaled back with no perceptible loss in performance, but consider this a "premium" office build that gets you a few perks you normally won't find in an off-the-shelf. Low noise is one perk...not that your usage will likely ramp up the CPU much, but all of those off-the-shelf desktops use stock coolers that tend to get loud under load. The acoustics of the case and the after-market CPU cooler will make it near silent (but feel free to pick a different case if you want). Also, the motherboard has an M.2 slot that supports PCIe 3.0 x4 (which means, when they come down in price, you could buy something like the Samsung 950 Pro SSD, which are several times faster than the SSDs you've worked with).

It also includes a legit copy of Windows, so that's $90 you could chop right away, if desired.