Newbie here - tow vehicle question?

2000 lbs is still a pretty light trailer. I'd look for something like an s10 or blazer if you need 4 doors. They're tough proven technology relatively cheap to repair and easily run up to 300k miles. Though I'd get one in addition to the civic. No reason to ditch reliability and 35mpg for 18 mpg for 2 weeks a year.
My 93 s10 is a 4cyl 5sp gets about 23mpg with 340,000 miles on it and has a 3500 lb tow rating.

Hairball got it.
If You want a full size pickup, the 1988 to 1995 Chevy and GMC are usually priced so a person can afford them.
My 1993 K1500 GMC has 270,000 miles on it and still performs like a champ. It gets 17 on a regular basis and in some conditions gets above that. The K rating means that it is four wheel drive, where You live in the N.W. that might prove to be mighty useful too.
I figure about 12 to 13 mpg when towing and the 350 V8 has plenty of power to handle it.
A relatively nice one can be had for around $3,000.00 and less if it has a lot of miles on it.
You might also consider a real nice one that might need a transmission, they usually go for a $1,000.00 or less then another 2 thousand to get a nice heavy duty transmission with all of the uprated components installed.
I like the extended cab so there is room for all of My survival gear in the back seat. It is about 16 foot long with the extended cab.

Thank you all!

Yup, more is better when it comes to towing or pulling.

Thanks, everyone! This info is really helpful.

One other option if it's really just a week or two a year? Rent a truck or suv from enterprise. It'll be about $250-350, there will be no older vehicle maintenance to do, no worries about breakdowns, no trying to fit a big vehicle and trailer on your drive, and the $20 extra per week you don't spend gassing up a truck/suv the rest of the year pays for the rental.