Second hand Iphone won't recognise sim or connect to home Wifi

You're saying two different things here...in your original post, you stated: "it's not recognising my sim card and won't connect to the internet or make any calls." Now you're saying it does recognize your sim(no error messages), but you can't get a signal and receive a "no service" message. These are entirely two different problems.

If the later is true, get a new sim card from your carrier. Make sure they are aware you will be using an iPhone on their network & such is provisioned properly. Turn your phone off, insert the new sim, turn your phone on...what happens?

Sounds like your phone has not been officially unlocked. Where did this phone originate? What carrier was it originally locked to? What carrier are you trying to use the phone with? How was this phone unlocked?

How to get it to recognize your SIM depends on what message you are getting. Does it say you have an unsupported SIM, or does it simply say no SIM is installed?

If the former, you're hosed. The phone is not legitimately unlocked. Return it to the person you got it from and get your money back if possible, or sell it and buy one from a legitimate source.

If it were rejecting the SIM card,you'd get a message that an unsupported SIM was installed. Who is you carrier and where are you? Do you have another phone you can put the SIM in to compare signal strength? On top of everything else, it's entirely possible that there is something physically wrong with the phone that it can't lock on to your network.

Have you contacted your carrier to make sure the network settings on the phone are correct? In addition, most carriers require an iPhone specific plan, including a data plan, for iPhone using customers.