Sure you can :)

I was on tight budget too but nowadays you can get pretty decent PC for web development.

Base specs: Intel i3 6100 + 8GB DDR4 RAM + 120GB SSD (SATAIII) + 1TB HDD

CPU - Intel i3 6100

RAM - Kingston HyperX FURY Black 8GB DDR4

Motherboard - MSI Intel Skylake B150 ECO

SSD - Kingston Digital 120GB SSDNow V300

HDD - Western Digital 1TB

PSU - EVGA 500 W1 80+, 500W

Case - Zalman ATX Mini Tower

In my opinion this is pretty decent budget build and it is $395.06. I intentionally made it under your budget because you have to weight what is most important to you and beef up that spec. If you need more horsepower than upgrade CPU. I didn't add monitor and peripherals. And one more thing, I think having a SSD is really helpful as everything works so much faster. Booting, copying, indexing, everything.

EDIT: If this is too expensive for you then I suggest that you go for used specs. I think that older generation i3 and 8GB of DDR3 RAM are the minimum if you plan to use this PC for at least several years.

I hope this can help you as a starting point at least, good luck :)

There's nothing wrong with a Mac Mini either, if you want a mac. Just get a Dell 24" and you're good to go.

Following up with @JanVladimirMostert get a Chip or Raspberry or stuff if you're doing database development. It's easier to find bottlenecks when your server chokes compared to having a full blown fast machine which you might not always have in production. But it highly depends what kind of software you're building. Like @IvanBernatovic i'd say enough RAM (16GB+ if you use virtual machines) and a decent enough CPU to keep your IDE in the air. And those can consume quite a bit of both, depending on how many features you use. (don't start the holy war on me folks; notepad doesn't require much as well ;) )

Get at least an i3 or quad core AMD, at least 8gb team (16 of you need VMs) and as big an SSD as you can afford. You can skimp on almost everything else.

A Mac mini might be an option, used may be better, if you can upgrade RAM and storage. Newer models are much more limited.

If you have a working computer, less than 5yo, just max the ram, get a 480gb ssd… and do a fresh install of your OS.

I used to order the parts separately directly from the importers and just build a PC from scratch. My desktop PC is still a custom built PC running Linux to avoid licencing costs of windows. As long as you have a decent amount of RAM, most modern hardware, even in the low-end range should do just fine for dev.

I used to DEV on an overclocked Pentium MMX 166MHz (overclocked to 200MHz) with 32MB of RAM while the rest of the world were bragging with their 1.5GHz PCs with many times more RAM than I had. Compiling in Delphi took an hour, so my code had to be perfect first shot, but that didn't stop me from DEVing. So you can make almost any hardware work for you, even a Raspberry PI can work fine for a DEV machine if you really need to stretch the budget.