You can actually build a decent enough computer for the budget you have and if possible you can always upgrade it later.

I wouldn't go for an integrated GPU as you can get some decent ones fairly cheap.

But the first thing I would suggest is to go for AMD Ryzen rather than Intel. Ryzen is "killing" Intel when its comes to multithreading unless you are willing to pay a lot more.

AMD Ryzen 5 3600

6 Cores - 3600 MHz - 65 watts

From $ 159.99

This include a CPU Fan as well.

Intel Core i7-9700K

$374.00 - $385.00

And then you have to buy a CPU fan as well.

So you can get a Ryzen which outperform Intel for less than half the price.

For the money you save you can buy a motherboard as well.

MSI MPG B550 Gaming Edge WiFi Gaming Motherboard (AMD AM4, DDR4, PCIe 4.0, SATA 6Gb/s, M.2, USB 3.2 Gen 2, AX Wi-Fi 6, HDMI/DP, ATX) $224.88

16 GB memory around 100 $

If you already have a ATX cabinet you can use that, you might have to get a new power supply, depending on what you have.

For graphic card you can get a Nvidia 1660 super RTX with 6 GB for $270 (This you can buy later or something else.)

Throw in a SSD (Samsung 1 TB $139.99)

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AMD Ryzen 5 3600

MSI MPG B550 Gaming Edge WiFi Gaming Motherboard

16 GB memory

Nvidia 1660 super RTX with 6 GB

SSD 1 TB

That would put you at 895 $

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AMD Ryzen 5 3600

MSI MPG B550 Gaming Edge WiFi Gaming Motherboard

16 GB memory

Nvidia 1660 super RTX with 6 GB (Buy graphic card later)

SSD 1 TB

That is 625 $

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(Depending on what power supply you have or if you need to buy an new cabinet as well, you will have to put that on top. And you probably need to buy windows 10 as well.)

(I myself have the following computer running fine with a 500 watts power supply.)

Ryzen 7 3700X

32 GB memory

SSD 256 GB

SSD 1TB

External HD 1 TB

Internal 500 GB HD

TUF Gaming x570-Plus motherboard

Nvidia Geforce 1660 super

And you can probably search a bit around the internet and find out how you can save some more money or adjust the stuff I suggested.