EU Spouse & Ancestry

My wife is an EU citizen, and my grandmother was born in the UK.
Can anyone tell me if either/both of these factors would expediate the immigration process?

European citizens
EEA & Swiss nationals (INF 18 )
Chapter 21 - The European dimension

United Kingdom ancestry
UK Ancestry (INF 9)
Chapter 18.6 United Kingdom Ancestry

I wonder what you mean by "the immigration process" - are you considering settlement in the UK?

Both routes, as described in the links provided by Vinny can lead to settlement.

One significant difference is that applications made under the EEA regulations for a Family Permit to enter the UK, and a Residence Permit to stay here, are free of charge. An application made under UK Immigration Rules for Entry Clearance under the ancestry provisions, and the subsequent application for ILR, cost several hundred pounds.

As against that, your status as an EEA Family Member would be dependent on your wife. If she didn't want to stay in the UK, or god forbid, you separated, you might have some difficulty establishing permanent residence here. If you qualify under UK ancestry, you could acquire permanent status here in your own right. It's pretty cast-iron, because you're never not going to have had a UK grandparent, if you see what I mean.

Up to you

The plan, indeed, is to settle, and thank you for pointing out that important difference.

It seems very simple going the EEA Family Member route. Do you know if the permanent residency status one could obtain by these means is limited in any way? Would I have the right to study as well as work? Could I apply for a student loan in the UK?

Just to be clear about "Permanent Residence", that is what you would acquire after spending 5 years here with a Residence Card as the Family Member of an EEA National.
Having acquired a Residence Card you would be entitled to work or study here.
I'm sure you would qualify for a student loan once you have Permanent Residence, but perhaps someone else could advise you about the entitlement of Family Members to this, because I don't know.

Mr Rusty wrote: If you qualify under UK ancestry, you could acquire permanent status here in your own right. It's pretty cast-iron, because you're never not going to have had a UK grandparent, if you see what I mean.

But Ancestry could always be closed to new applicants.