What you are paying for from Origin is nice aesthetics (which do nothing for performance) and lifetime labor (even for user requested upgrades). This life time labor warranty is certainly very nice, but unless you buy an upgrade warranty, the parts are only warranted for 1 year. If you build your own, you get the warranty from the maker which could be 3 years for the motherboard, lifetime on the RAM, and up to 10 years on the SSD. But also, in the world of computers, lifetimes don't last a lifetime because technologies are superseded too quickly. There's a good chance, for a example, an upgraded CPU or RAM you want is not supported by your motherboard. So you have to start all over.
You also only get free shipping during the warranty period (if you live in the US). Free shipping is nice, but takes time and there is always the very real risk the box will fall off the FedEx truck during shipping. Shipping a computer after the warranty runs out is expensive.
It is because the computer has to go back to Miami for all warranty or free labor work that I would not recommend buying from them - unless you live in the Miami area and can transport it yourself.
Building your own really is much easier than it sounds - you really are just assembling parts and connecting cables. And with that budget, you could certainly build a very nice computer - with a keyboard, mouse and maybe monitor too! But if building your own is just not something you really want to do (and there's no shame in that), I would urge you to locate a local custom PC shop to build it for you. A place where you can establish a personal relationship and report with the tech doing the building. A person/shop that has a personal interest in pleasing their customer.
I note you said you want Origin to build this because you want to finance the build. But I don't see where Origin has a payment plan. That suggests you will arrange financing another way - perhaps through a credit card. Well, Newegg and Amazon take credit cards and I am sure a local shop will too. And many credit cards automatically double or at least extend the warranty on many purchases.