Confused with setup?

Ive been looking at moving over to Asterisk for some time but haven really had the need, and using vonage was cost effective.

Now we have three office, one in the UK (with one employee) one in western Australia (with two employees) and the other on the East Coast of Australia (with three employees).
Im still unsure how would be most efficient and cost effective, i don’t see the need to have a asterisk server at each location.

Im not sure if this is possible, but i would like to remotely host a asterisk server (as none of the office ADSL connections would be suitable for hosting) then have a range of IP voip phones and standard phones connected to a voip adapter in the various offices that can then connect to the server.

Is this possible and what would be the best way of doing this?

Host your asterisk server on cloud

Hosting the Asterisk server in the cloud would address part of the problem, but if the OP wants to link into the local PSTN using analogue phones at each location, this could be done by having an ATA at each location which are registered with Asterisk. Register each of the ATAs with the central Asterisk server and you should be able to set up an internal phone network covering the three offices, and have the ability to pass calls out onto the PSTN at each location to avoid international call charges.

I had an arrangement like this before I got an analogue card on my asterisk box - I used a FritzBox 7270 router/ATA to provide the link to the PSTN and registered Asterisk as a SIP server and an extension off the Fritzbox. This meant that I could pass incoming PSTN calls to Asterisk and the SIP phones, and allow Asterisk to pass calls from the SIP phones via the Fritzbox onto the PSTN (or to the local Analogue phones). Having multiple offices would complicate the arrangement a bit, but it should still work.