The aforementioned May 2/3 High Performance Driving and Competition Licencing school would be your best bet to get your racing licence. The school is conducted over two days at race city and will feature on track, classroom, and skidpad exercises (on the oval pad). In addition to in car instruction on the track you will also be able to participate in three mock race starts with a full grid of cars at the end of the second day. As for your race licence there will be a short written exam held in the classroom at the end of the school, those who pass (don't worry its not a difficult test) will be eligible to apply for their racing licence. Cost for the two day school is probably in the realm of $450 I think... but I'm not 100% sure on the exact price. In all honesty for the amount of track time and one-to-one instruction you get its a heck of a deal!
As for your Honda Civic I believe it would fall into the class IT2 or ITGT or something like that. You can look at the applicable rules for classification on the WCMA website and mull over all the intrinsic details. Both IT2 and ITGT are very large and very well supported classes so you will have plenty of competition to race against in class. I'm sure some of the Honda racing Gurus can place your car better than myself... hopefully one of them will comment soon.
In regards to funding and experience, yes racing can be expensive but most individuals can make due with a rather minimal budget. I myself race a 1984 Mazda Rx7 in the Challenge Car class and my operating costs are about as low as you can get. Several racers do not compete in every race event and thereby can afford to attend the amount of races in their budget range. Experience is not a worry. It sounds like from your beyond.ca posts that you have a healthy dose of driving experience from autocrossing and besides, all rookies have a warning triangle placed on the back of their car to alert other drivers or their racing inexperience. Every rookie I've talked to was scared to death of the first race, but generally speaking after that they were hooked and excited for every other race start and event.
Lastly yes you will need some safety modifications on your car. The most pain in the ass and costly is a full roll cage that is WCMA Tech approved. Additionally you will need a small fire extinguisher ($15 bucks), battery kill switch ($30), race seat ($varies), 5 or 6 point racing harness ($100) and then your Nomex racing suit and approved racing helmet. I purchased my seat, helmet, and racing suit off EBay for quite a low price. Depends how good you are at scavenging deals and such.
Well I hope that helped, if you have any other questions just shoot away.
-M