The Raspberry Pi Zero does not come with an ethernet port. For my experimental router project, I need to connect the Pi Zero to a wired network where the Pi Zero will act as a router for many computers. I can use a USB to RJ45 adapter for this task, but I may need something faster. What is the cheapest way to achieve high speed ethernet connections?
To summarize the comments in an answer: if you want real gigabit throughput you cannot use any Raspberry Pi. The RPi Zero is the worst candidate. 10Mb would be more realistic. Raspberry Pi USB's are USB2.0. USB2.0 has an absolute theoretical maximum speed of 480Mbit - though, in reality you'd be lucky to get 300Mbit - and I dare say that would be half duplex - about one sixth of what you would want for gigabit ethernet. You may look at using the new Pi 3B+ which comes with Gigabit Ethernet over USB 2.0 (maximum throughput 300 Mbps).
Cited from the comments of @Milliways, @Jaromanda X, @HeatfanJohn, thanks.