The 7446/7 is a decoder with 4 binary inputs and 7 segment output. However it only works for 10 counts (0-9) of the 16 available with 4 inputs, so should be driven by a BCD (binary coded decimal) counter. This is something you can look up. Also it is a TTL family device, so you need the 74HC46/7, which works with 5V or less. Consider using the HC CMOS logic family with a 5 volts supply, then the 74HC47 or a TTL version is CMOS compatible.
However, the 4020 is a binary counter, so not suitable. Also not all outputs of the 4020 are available for BCD display. Generally one decoder is used for each decade, driving one display digit, and the count goes in 10s. If it is binary the result is useless. It might be possible to use it to display just one digit with binary inputs, the last 4 for example. It depends what you want.
A CMOS pair are the 4510 BCD counter and the 4511 decoder. As this counter can be preloaded, it can count up or down, and the carry output is the timer out. It is usually a down count loaded with BCD switches, so the time can be loaded without doing arithmetic. (See the first link). Look up BCD to 7 segment decoder data sheets to find the type to suit your display. Look up the BCD counter data sheets for more application data.
Yes it takes plenty of chips, and wiring. The alternative is to use a microprocessor, probably cheaper with a suitable PIC type for example..