There are some elements of your situation that work in your favor. It may be possible.
For one thing, it sounds like you’ll be working entirely “in the box”. Silence is typically one of the main cost and component drivers of building a music computer. It comes up again and a again: fan noise, HDD noise, power supply noise. To keep the power supply quiet, people resort to expensive cooling systems (typically liquid), or a fanless PSU (power supply unit). I have a fanless PSU, and I can tell you that they can only deliver so much power. An additional graphics card is therefore a dubious proposition for me. I also have a special noise-damping case with oversized super-quiet fans and large internal air volume. I use a SSD to avoid HDD noise. None of these expenses would seem to apply to you, but it looks like you’ll probably want to buy a graphics card.
You should seriously consider putting together a computer from parts. This will save money in general, but it will also allow you to save on the components that are non-critical to your use scenario(s). DAW host computers typically need a lot of CPU/RAM power. When you go to the mainstream market, the closest match is often a gaming system. There’s some mismatch in there. You don’t need flashing LEDs or a resources-hungry graphics card to simply edit video. You just want to offload some of the work from your CPU. Putting together your own computer isn’t terribly different from building something out of Legos. if you’re too anxious to give it a go, a local shop will probably do it for you quite cheaply, .
Building your own machine may solve the financial problems, but it introduces a component selection problem. The most important of these is your choice of motherboard, but that’s generally not the right place to start. Start by looking at the software you wish to run. OK: Cubase, East-West, bunch of plugins, something for video editing, probable second monitor. We’re looking at the usual brute strength CPU and RAM as you seem to have figured out. Now, a typical i7 has a GPU embedded in the chip, so you can probably delay a graphics card purchase until it becomes clear that there’s a problem. OTOH, you need to plan for that contingency. Look at the user forums for the software you plan to use so you can figure our which graphics cards have the best and worst compatibility. You need to do this to avoid headaches down the road, and to figure out your possible future power requirements so that you won’t have buy another power supply down the road. Then there’s the HDD/SDD issue. HDDs are cheaper but slower. A SDD is preferable in general. If you go for the SDD, get a good one – something highly rated from Samsung. SDDs suffer from power outages, so you might want to get a UPS (uninterrupted power supply), which is a separate box. Don’t get one that puts out an iffy sine wave of AC. I recommend Cyberpower. This additional expense is part of the downside of SSDs. Still, go with the SSD if you can afford it. (I suppose you could switch over from HDD to SSD in the future to save money now. It’s a pain, but Samsung has software to help with that.) Finally, we come to the motherboard. It will probably come down to a small number of choices. Asus is a likely candidate. The ROG = republic of gamers seal of approval is worth a lot here, since those guys are pretty thorough when it comes to motherboards. ROG isn’t crucial, but it’s a good sign. The mobo has to be compatible with your CPU of choice. And that’s about it.
Another factor in your favor is that you already have a computer, so you don’t really need to beef up your new machine to run youtube etc. in the background. It’s usually a good idea to keep your DAW host from free-ranging on the internet, which is asking for trouble. Why not get a KVM switch and use your old machine for browsing, office work, and so on? KVM (keyboard, video, mouse) will allow you to switch between machines without the clutter and expense of extra keyboard, video monitor, and mouse. Keeping your old machine in service will not only help protect your DAW from needless internet exposure, it will decrease the load on the new machine, and therefore the initial cost.