各位英语好的给看看，打官司是不是要提前缴纳好多费用啊？万谢!

收到了律师事务所的来函，那合同和他们预先说的完全不一样。
他们让我送材料时，声称对这个案子感兴趣，还说“官司赢之前，你是看不到任何帐单的”也就是“不赢不收费，赢了收三分之一的费用。” 我读了一下这个合同，怎么感觉里面净是陷阱啊。
各位英语好的给看看，是不是要提前缴纳好多费用啊？万谢!

Contract of Representation

I hereby agree to retain and employ, Mack Smith as my attorney to prosecute or settle all claims against RED RIVER HOSPITAL, who shall be liable on account of damages, which resulted from potential medical malpractice. In consideration for services rendered and to be rendered, I agree to pay my attorney a sum equal to 33% of whatever may be recovered from said claim either by suit, settlement, or in any other matter.
It is further agreed that in addition to the above attorney’s fees, all court costs, subpoena costs, photos, depositions, and court reporter costs, reports, witness statements, and other costs that the above named attorney may be required to advance on my behalf in connection with the representation shall be paid by the undersigned client.
I further agree that from the proceeds of any such recovery, whether by settlement, judgment, or otherwise, you may deduct the attorney’s fees to which you are entitled, together with all costs and expenses that remain unpaid.
It is understood that any payment to you for such services is entirely contingent upon your making recovery of money or property for me or on my behalf.
诸位，看在我辛辛苦苦一字一字把合同敲出来了，而且被催着签字的份上，给点建议啊！
万分感谢！