How to give priorities to Interrupt handlers in a normal linux kernel?

Question

I am working on precise time stamping of packets being captured from a network. An interrupt is generated at every packet reception. Thus an interrupt handler registered by the Ethernet driver queues the captured packets. I have 2 questions

1. Who performs the time stamping on each packet, the interrupt handler or the kernel which processes the packets from the queue.
2. Depending on which task (interrupt handler or kernel, both being in kernel space) performs the time stamping, how can I increase its priority in a normal kernel (i.e. without using a RT kernel)