My suggestion to you #1 is pull your credit reports. Since you have been denied you are legally entitled to a free report by all 3 credit bureaus. Contact them for one. See what is on your report that could be negatively affecting your ability to get a credit card. If there is anything negative - dispute it. Dispute anything from incorrect balances, to credit collectors, etc. This can open up a small can of worms and wake up dead creditors if you have any sitting there, and depending on what is on your credit report - so head over to creditnet.com and creditboards.com for more help on that. You'd be amazed on how much getting one item deleted from a report can raise your score!
#2. If nothing negative on your reports, don't bother with loans. Why pay interest to get credit. Credit is supposed to be a tool, not put you in debt! Go to a local credit union, or search online for a bank that will give you a secured card. Usually after putting your own money down on a secure card and keeping it in good standing for a few months, the bank will upgrade you to a normal credit card, or at least give your score a chance to grow to allow you to get a credit card on your own. Most likely you will only qualify for "sub-prime" cards, crappy interest, money down, etc. So my suggestion is stick to the prepaid secure cards for a while - then repull your credit to see what your score is and go to www.whogavemecredit.com to get an idea of what you can apply for. It's not an exact science, but more of a guessing game - but that site can give you a better idea of what you might qualify for.
#3.) For a really fast credit score boost, have a close family member or friend (be careful with friends money) with good credit add you as an authorized user to one of their credit cards. Make sure the card doesn't have a large balance otherwise that could hurt you more. Also make sure the card has history. When your added in as an authorized user, automatically 2 years of their credit past are added to your report - so obviously paid on time credit cards prefered, since if they are 30 days late etc, that will reflect on your account.
In this day and age, everyone needs at least one credit card for emergencies, etc. Work up your credit to get to that point and get yourself a good card. Don't settle just for sub-prime if you don;'t have to. If you can wait it out a little longer, take my suggestions above and start there. Patience is a virtue, but I tell you after 6 months I increased my credit score 100 points and now have quite a few good rate credit cards, with fat limits.
Good luck!