Still no carrier gives you a 2nd line with a different phone number. But since the last post, things are a lot different.
If you buy direct from China, you have dual SIM card GSM phone for cheap, almost half that of my refurbished unlocked GSM phone many years ago. They use those phones when people travel, it's much cheaper to just get another SIM from the convenient store than to do cross border roaming. So you have two independent lines on a single phone, active all the time. So you don't need any magic dual sim adapter unless you still don't want to part with your old GSM phone.
The other way is of course to buy a smart phone from China, and the only choice is Android. Typically they have two sims because of the same reason above, and that it is popular to have one sim for voice, and another for broadband. So you can say money when you don't need broadband all the time. But both sim's are fully functionally.
The easiest, anywhere, is that you buy a smart phone. In Android you have Google Voice app bundled, and you have the app in iPhones. This app is pretty integrated in Android. You can set that international calls will be using Google Voice alone. Or any phone or text you send, you will be given the option of which number to use. Or of course you can start GVoice to use the other number. Also, you Google number is live all the time, direct to your phone.
You just need to signup for a Google Voice account and then ask for a new number. It's free and "permanent" except for international calls. But I think Google Voice is only available in US. The only problem is that you use Google number as your main number. I don't know if the app deals with a 2nd Google number. Also, the rule is one mobile number for one Google Voice account. You can redirect the numbers how you want it, but you need two mobile numbers to register for two accounts.
Skype is in disarray one year on. It's probably because Skype has been using a sophisticated encryption intended for desktops years ago, and it's P2P, requiring extra processing than just the calls. Typically they work but not well for the latest Android phones.
If you don't want to scrap your old phone because of the phone list, look if it supports Bluetooth. Most does. You just need to enable it and the new smart phones can import the phone list directly.