There problem is man these cards are hard to get. I was thinking Ok, the game is discontinued I can get the cards for super cheap and people will practically want me to take them off their hands. This is not really the case. It seems there are lots of folks still looking for the cards and they are often selling for near retail value online. This has been a bit of a shock for me. I certainly am not going to invest huge sums of money in this project and I figure you may feel the same way. So I am going to try to help you do things econo.
There are some things to know when you start out. First off Vampire the Eternal Struggle and Jyhad are the same game. They have just been rebranded which means the card backs look different. At first I was upset by this, thinking I would only want Vampire VTES cards. Your best deals are going to be on Jyhad cards so turning your nose up at cards is not the thing to do if you are on a budget. You can always get backed sleeves and everything is fine. One thing to note is the cards often have a different look in VTES as their were many updates. You will notice many early Vtes cards look like the Jyhad versions and the later ones look very different. They play the same.
Keeping all that in mind the first place I think you should look is ebay. There are many auctions often for starters priced more than their retail price. I am going to urge you to look at pkp310 who sells his own pre constructed beginners decks. He will sent you a deck for each of the basic clans all are ready to play. This gives you a nice leg up as the decks can get you started right away. They play in the general them of each of the clans so will give you an idea of what you like.
Next I would say you have two options. You can pick a clan you like and ebay a few starter decks and look for constructed starters online. The other option is to start hunting through your local game, comic and video game shops. For eBay you are going to find there are usually a couple of constructed decks for every clan. There was a release of the clan decks around third edition. You can also go with the Antribu versions of your caln as well. The vampires included will be sabbat but the disciplines will be mostly the same. So they will function similar with a few flavor differences for Sabbat vs Camarilla.
If you are picking through you local game and comic books shops, good luck. I have been able to score one great deal and nothing else. It was a box of bloodlines for 9 dollars. Other than that the shops have been barren. I would suggest you call around and may be prepared to travel a bit. I live in the silicon valley and checked with our three main game stores and have been checking comic book shops when i can find them. I am also planning to check out a couple of game stops that I remember selling cards but those are far down the list. I will only hit them when i am in the area.
The last idea is hitting up friends who once played Jyhad or Vtes and the game cons I am thinking that is a bit of a hail mary as the cons will probably have people who value the cards and will try to sell them for their highest value. Still you can do ok on ebay if you looking for straight Jyhad cards so you may need go that direction if you are planning on constructing lots of decks.
If you are planning on going for some of the odd clans you should keep in mind their seem to have been two sets that focus each of the groups. So you have these odd pairs like Final Nights and Ancient hears both giving focus to Assamites and Followers of Set. The Sabbat and Black hand sets give support to Antribu versions of the standard clans. The bloodlines vampires get support in Kindred's most wanted and Heirs to the blood. Lords of Night gives you more of the Giovanni and Ravnos from Final nights. Legacy of blood and Ebony kingdom pair to flesh out the Liabon. Finally there is Blood Shadowed Court which is a reprint product that gives you a bunch of vampires. As I understand it you only need one starters box to have the full set of 100 reprinted vampires. If you are new, like me, this sounds good as it gives you a nice boost on your options.
Well that's it for now hopefully playing will go well and hopefully I can track down a couple of deals. Good luck on your hunting.