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This is the fourth post in a monthlong series that started here. Each post will take about two minutes to read and may include an action item that takes the reader another two minutes to complete. I am writing this for an audience of people who know nothing about frequent flyer miles, and my goal is that by the end, you know enough to fly for free anywhere you want to go.

There are currently some huge sign up bonuses that folks new to the miles game can pick up.

I’ve categorized some of the best offers below, but before applying for any cards, I recommend checking out my Introduction to Travel Credit Cards from yesterday.

I also recommend getting a Free Credit Card Consultation instead of picking cards on your own. It breaks my heart when people come to my Award Booking Service with the wrong miles for the trip they want. There’s no reason to Make the Biggest Mistake in Our Hobby.

• What are the best cards for beginners?

Best Card for Economy Travel

Arrival Plus

The Barclaycard Arrival Plus^TM World Elite MasterCard® is a great card for families that travel in economy, since Arrival miles can be used to book any flight on any airline with no blackouts. Miles can also be redeemed for any hotel or other travel expense.

This card comes with 40,000 bonus miles after spending $3,000 in the first 90 days and earns 2 miles per dollar on all purchases.

Miles are worth 1.14 cents each, so spending $3,000 on the card in the first 90 days earns more than $500 in free flights or other travel expenses.

With this card you can book any flight on any airline at any time, or any hotel, or rental car, then redeem your miles for a statement credit equal to the cost. Here’s how.

The 40,000 bonus miles could be used on any $400 flight without the need to find award space. You would even earn miles for flying the flight, since the airline will see it as a cash ticket!

Plus you get a 10% rebate after every redemption for travel, so after redeeming the 40,000 miles for $400 in travel, you get 4,000 miles back, worth $40 more dollars.

I have used my Arrival miles on a recent trip to book a motel and domestic flights like a $150 trip from Raleigh to Tampa that would have been a poor value with traditional miles.

This card fills the gaps in a miles strategy because the rewards are perfect for cheap domestic flights or hotels that otherwise would be bad redemptions with traditional airline miles and hotel points.

There is no annual fee the first year, $89 thereafter.

Application Link: Barclaycard Arrival Plus^TM World Elite MasterCard®

Best for Asia, South America, and Central America

Citi Executive / AAdvantage World Elite MasterCard

With recent devaluations to the United and Delta award charts, American Airlines miles and US Airways miles are the most valuable miles for now.

American Airlines miles are the undisputed best miles for ultra-luxury redemptions, and the miles are valuable for trips to Asia, South America, Europe, and Australia. On a recent trip, I spent 67,500 American Airlines miles for a First Class redemption from New York City to Singapore with 23 hours in Macau along the way.

Citi offers the American Airlines Executive Card with 75,000 bonus miles after spending $7,500 in the first three months.

Beyond the sign up bonus, cardholders also get free lounge access in American Airlines lounges worldwide.

The card has a gigantic $450 annual fee, though it is partially offset by $100 in statement credits on your first $100 in purchases on the card.

The landing page for this 75,000 mile offer has been take down, a possible sign that the deal will end soon. Here is a direct link to the 75,000 mile offer, which does not mention the card’s bonus. Folks report applying through that page and getting the bonus. Your miles may vary.

Best Business Card

Ink Plus and Ink Bold

The Inks are business cards that offer 50,000 Ultimate Rewards sign up bonuses after spending $5k in the first three months. Ultimate Rewards transfer 1:1 to United, British Airways, Korean, Southwest, Virgin Atlantic, Hyatt, Amtrak, and more.

The Inks earn 5x points on internet, phone, and cell phone bills; 5x points on purchases at office supply stores; 2x points on hotels and gas; and 1x points on everything else.

The Inks have no annual fee the first 12 months, $95 thereafter.

The Ink Bold is exactly the same as the Ink Plus except the Plus is a credit card and the Bold is a charge card. That means the Bold must be paid off in full each month, while you can run a balance on the Plus. Because of this difference, I have gotten both for the same business.

I used Ultimate Rewards (transferred to Hyatt points) to book the Grand Hyatt Macau and Ultimate Rewards (transferred to United miles) to book Slovenia-to-North Carolina in Lufthansa First Class on a recent trip.

Best Card for Small Spenders

US Airways Premier World MasterCard

The US Airways® Premier World MasterCard® is now offering 40,000 bonus miles after first purchase. US Airways miles are the most valuable miles right now because of how cheap business class awards are on the US Airways award chart.

The other big perks are a 5,000 mile discount on awards booked entirely on US Airways metal and a free checked bag for you and four companions on paid US Airways flights purchased with the cards.

The card earns 1 US Airways mile per dollar on all purchases and 2 miles per dollar on US Airways purchases.

There is an $89 annual fee.

US Airways has an incredible award chart to use the miles now, or they will be converted to American Airlines miles during the merger, which is a fair conversion.

This card will disappear in early 2015 when US Airways’ and American Airlines’ loyalty programs combine.

Application Link: The US Airways® Premier World MasterCard®

Best All Around Card

Sapphire Preferred

The Chase Sapphire Preferred is a personal card that earns 40k Ultimate Rewards after spending $3k in 3 months. Ultimate Rewards transfer 1:1 to United, British Airways, Korean, Southwest, Virgin Atlantic, Hyatt, Amtrak, and more.

You also get 5k bonus points for adding an authorized user while applying, so I think of this as a 45k bonus point card. (Adding an authorized user does not prevent that person from getting the card at the same time or in the future as a primary account holder and getting the full sign up bonus.)

The Sapphire Preferred earns 2x points on dining and travel. Dining includes bars, restaurants, and fast food. Travel includes airfare, hotels, taxis, rental cars, tolls, parking, and much more.

The other big bonus is a 7% annual points dividend each January on all the points (other than the sign up bonus) earned in the previous calendar year.

The Sapphire Preferred has no annual fee the first year, then $95 thereafter.

Best Hotel Card (Limited Time Offer)

Citi Hilton HHonors Reserve Card

The Citi® Hilton HHonors™ Reserve Card is the best card for giving you free luxury hotel nights. The card comes with two free weekend nights at Hiltons worldwide after spending $2,500 in the first four months. The free nights are best spent at top-tier Hiltons and Conrads that can go for $500 or more per night.

For a limited time, the card even comes with a $100 statement credit if you spend $100+ on a Hilton stay in the first 90 days after getting the card.

This card is perfect to get aspirational stays at top tier properties like the Conrad Koh Samui that goes for 95,000 Hilton points per night and costs more than $1k per night.

The card also comes with Hilton Gold Status, so you can enjoy free internet and breakfast on those free stays.

The card earns 10x points on Hilton stays, 5x on airlines and car rentals, and 3x on all other purchases.

There card has no foreign transaction fee. The annual fee is $95.

Application Link: Citi® Hilton HHonors™ Reserve Card