Hi Jarek,
The HP solution that you've given is basically a series of lightweight access points - these are controlled by a central controller unit.
Cisco has two solutions - unfortunately, because you have more than 6 APs in mind, you'll need to go for the more expensive of the two. Depending on what you order, the Cisco 4402 Wireless LAN Controller supports up to 50 access points (the most basic option supports 12, which would do nicely for your setup).
The APs themselves would be AIR-LAP1131AG-x-K9 LWAPP.
I'm not sure about pricing for these units though.
As for your switches, you could use 4x Cisco WS-C2960-48TT. This will give you 192 ports. If you want to power your APs from the switches, then you would need to use either WS-C3560-48PS-S or WS-C3750-48PS-S.
If you don't want to use Power-over-Ethernet to power your access points, remember that the APs might not come with an A/C adapter (or, they come with an A/C adapter and you find that the position the APs have to go to is short on power cables). You can buy a power injector to supply power to the AP without having to use a PoE switch.
I hope this is of some help to you.
Kind regards,
Graeme