Creating subnets

Depends how many ports you need and how many networks. You may be better off using a basic layer 3 switch and use a consumer router to do NAT and such to access the internet. A true cisco router with more than 2 ethernet ports gets expensive fast. You could get a used cisco 3550 switch for less than $100.

You could also try a consumer router and load DD-WRT on it. You will need to be sure to read though the list of supported routers. You are going to need one that supports "port based vlan" This allows you to assign each lan port in the router to different vlans/networks.
Not all router chipsets allow this some will force all the lan ports to the same network. The vast majority of the routers people say have this ability are linksys...but not all.

So with a switch I will be able to create 2 sub networks? I want to connect accountant computer to one sub network and other employees to the other sub network.

With that cisco I think the limit is around 1000...not that it is useful to do that

If you were to use the switch you would still need a router since a switch can't do nat. A layer 3 switch is a mutliport router than do everything except stuff like NAT.

You would put in 3 subnets.

You would build say 3 networks

192.168.1.1/24 say for network 1
192.168.2.1/24 say for network 2
192.168.3.254/24 for the router network.

First you would set the default route on the switch to point to the router lets say it is on 192.168.3.1

You would define the DHCP pools on the switch to give out ip to the pc setting the switch at their default gate.

The switch when then handle all the routing between the 3 subnets.

If you're gonna have to look at purchasing equipment anyways to get this working, I'd suggest just getting a Sonicwall TZ 100 firewall appliance. Not only is this an business grade router, but you get added benefit of firewall protection and control, plus you can set up to 4 internal zones which will each work exactly like a VLAN. We have done this at my office and a couple other places. A TZ 100 is going to be the same price or cheaper than a Layer3 switch, but you also get the added routing and firewall capabilities all in one.

With this setup, all you need to do is configure your firewall with three LAN networks, for example:

X0: Management LAN - 192.168.0.0/24 this is the interface that you can gain access to the management side of the firewall and keep it separated from the rest of the network.
X1: Default WAN - goes to your outside modem or internet connection
X2: Accounting LAN - 192.168.2.0/24 this connects to your switch with an untagged or access switchport VLAN for your Accounting network.
X3: Staff LAN - 192.168.3.0/24 this connects to your switch with an untagged or access switchport VLAN for your Staff network.

Is there any device with let's say 8 Ethernet ports? Currently I have 3 computers connected to network, but soon there will be 3 more. Would it be reasonable to but device with more Ethernet ports or use a switch?

For the number of computers you are talking about, I'd recommend getting a separate switch for connecting to the individual computers to give you plenty of room to grow. Most all routers are going to have five or fewer ethernet ports. The Sonicwall TZ 215 and NSA 220 have up to seven gigabit speed ethernet ports, but that's still not ideal. Your best bet is to get a separate switch and router, even if you are going with a layer 3 switch.