There are 3 main considerations when we consider buying a perp:
1. How safe is the issuer. Government bonds from important countries should theoretically be safe (not so sure anymore). Also big reliable companies in defensive sectors. Beware of banks, though. Under the Basel-III requirement, an international capital standard, perpetual bonds or AT1 securities are more of a quasi-equity obligation. If an issuing bank incurs losses in a financial year, it cannot make coupon payment to its bondholders even if it has enough cash. Moreover, if the equity capital of the issuer falls below 6.125%, the entire investment of bondholders would be either written down or converted to equity.
2. Currency. You want to receive the payments in the strongest currency possible. Avoid emerging market currencies.
3. Interest rates. The price of these bonds strongly depends on interest rates. To calculate the price we just divide the annual coupon by a discount rate. For example, if a bond has a coupon of 8000 USD a year and we use a discount rate of 4%, the price of the bond should be 200000 USD. However if interest rates go up to 8%, the bond price is half the previous one.
It seems a very risky investment, but it doesn't have to be. If the coupon is high enough and the issuer is a reliable company that pays in dollars, in a few years the coupons will pay for the initial investment, and after that the investor and his inheritors just receive some nice cashflow forever.