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 :)