Well since you are doing budget builds, and you are also valuing smaller the better, my recommendation is the following,
CASE n PSU: Antec Mini-ITX Case ISK110-VESA $75
You can get $25-40 cases and $40-55 decent PSU, but here you will get both for a very similar price and a very small factor case, with a very efficient PSU, good enough for pentium or i3.
CPU: Intel Pentium Processor G3420 3.2 GHz LGA 1150 BX80646G3420 $70
Or the G3220, the only thing is that its sold atm for like $68, so for $2 you get 200mhz.... i bought mine at $50 sale, but atm is way to close.
Motherboard: ASRock H81M-ITX LGA 1150 Intel H81 HDMI SATA 6Gb/s USB 3.0 Mini ITX Intel Motherboard $60
There are a lot of alternatives, but thinking on a budget build, seems very good for the money.
Memory: Crucial Ballistix Sport Very Low Profile 8GB Kit (4GBx2) DDR3-1600 1.35V UDIMM 240-Pin Memory Modules BLS2C4G3D1609ES2LX0
This is low profile and low voltage memory, no need to go for tall memory heatsinks, but crosscheck compatibility with the motherboard you end up chosing. Just its not in stock atm from amazon, usually sells around $75.
SSD: Crucial M500 120GB SATA 2.5-Inch 7mm (with 9.5mm adapter) Internal Solid State Drive CT120M500SSD1 $70
You could even go for 240gb version for $40 more
, highly recommended, as space is always good and specially in the future is better to have more than less, the price is fair imo, and the SSD of this gen get the best performance in 240/256gb range, the 120/128gb versions are crippled by design.
TOTAL = $350 or $390 with the 240gb ssd =)
The ISK-110 also allows for a second 2.5hdd, in case you want to add one for storage down the road, for example for one of your users they need bigger storage for their workload, so you can add a HGST Travelstar 5K1500 1.5TB 2.5-Inch Mobile 5400 RPM 9.5mm Internal Bare Hard Disk Drive 0J28001
and end up with a very big storage for such a small footprint case, and even better the ISK110 is vesa mounted, so if the users have monitors that allow for vesa mounting the computer will take almost no space in their desks.