I'm new to this, and any help would be appreciated.

BACKGROUND: I'm a student that only spends about $1,500 per month, and therefore I'm looking to rack up as many miles as I can through the initial sign up bonuses of credit cards.

QUESTIONS:
(1) What do "targeted" credit card offers mean, and how do they differ from non-targeted?
(2) I signed up for a Chase United Mileage Plus Explorer card and got the 30k bonus miles. Is there any way to cancel this card and sign up for it again to get the bonus again? (it says the bonus is not eligible for prior or existing members.)
(3) If I wanted to continue getting UNITED miles, what other cards / offers give united bonus miles, or points that will transfer to united miles? (I'm looking for large (20k+) initial bonus mile awards, as I don't spend much money per month.)
(4) Are there any cards that you can sign up for, get the initial bonus amount, then cancel the card and do it again?
(5) Which airline has the best frequent flyer program, in terms of getting the most miles the fastest without spending much per month on a credit card?

Thanks!

Welcome to Flyertalk! You will need to research, read and read some more to answer some of your questions for yourself. This can be a rapidly changing game, so we only know what is today, not what will be tomorrow.

1. Targeted offers are mailed, emailed or otherwise personalized. Non-targeted offers are open to everyone.
2. Head over to the United Explorer thread in the credit card programs and spend some time reading it. There is a 50K offer that Chase will usually match if you send them a SM (secure message) asking them to match the better offer, within a certain time frame. Officially, you can't get the bonus again. Some people have been able to by waiting a year or more after closing the card. Plan to check the relevant thread occasionally for datapoints.
3. Chase Sapphire Preferred, Ink Plus, Ink Bold, United Explorer Business, Chase Freedom if you also have Sapphire Preferred. Also, for now at least, US miles can be used for flights on United flights, and the US card has no spending requirement.
4. Yes. Each card has its own rules. BofA Alaska may be the most churnable card right now, but again, rules change.
5. United for most people, with so many Chase cards that earn United miles or UR points that can be transferred to, among other things, UA miles.

Find what works for you, read and read more, subscribe to some blogs and read what they have to say about redeeming miles efficiently. Be ready to jump on a great deal when it shows up, but don't worry if you miss one. And travel on your terms, to the places you want to go.

Welcome...

(1) They are offers sent directly to someone, based on some combination of credit profile and other data the issuer has. Sometimes only the recipient can apply, sometimes the same application will work for anyone.

(2) How long ago did you apply? Usually Chase will match a bonus offer within 60 days of your signup if you send a secure message. Otherwise, the prevailing wisdom is that it takes at least 2 years after cancellation to get the UA bonus again. However, you could get the business version, as that is considered a different product.

(3) Anything that earns Ultimate Rewards points - so much of the Ink and Sapphire families of cards. You can also earn in any Star Alliance partner's program which, for now, includes US. Their Mastercard has a 35k signup offer, and well as the fact that the SPG card's 25k can convert to 30k on US. (There are also cards for the "foreign" *A carriers, with lots of fees/restrictions that can trip you up if you haven't fully researched their programs.)

(4) Pretty much all of them, the only question is how long you have to wait. Check out the threads for each of the cards for guidance.

(5) None of them are particularly easy from everyday spend. There are folks who "manufacture" additional spend using a variety of methods. There are several UR cards that work well for that. You should spend some time calculating valuations of each type of mile/point - you may very well find that a 2% cashback card is more profitable for you, outside of signup bonuses.

EDIT: Look at that; two independent opinions that are essentially the same. Rare occurrence.

Thanks very much MDtR-Chicago and KennyBSAT! Very helpful.

To earn points (albeit slowly) sign up for e-rewards.com (various) and e-miles.com (Delta SkyMiles). You take surveys or watch videos and earn points.

Another trick with limited spending would be gift card churn--I imagine a college student should have no trouble putting a Starbucks gift card to good use. Find areas you get percent of point bonuses like grocery, gas, office supplies and churn cards from those locations.

If you have a flexible schedule you can watch the deals sections and fly cheap flights to unremarkable places like Omaha or Buffalo for cheap and possible rack up enough segments for elite status. As a student I used to interview at places I wanted to visit to get a free trip--interview in Burbank and visit LA, interview in Stamford to visit NYC, etc.

And also, never hurts to ask parents, relatives to donate miles to you.