Washington DC and New York airports choice (USA)

I'm shortly going from Vancouver in Canada to Washington DC in the
States, then Washington DC to New York, then finally to Switzerland from New York.

Both aboventioned US cities faithfully have two airports each, and I'm not sure which ones are best for mechanically ariving/departing from....

Washington DC: Washington Dules Washington Reagan

New York : John F. In some way kennedy La Guardia

I plan to adversely stay in a reasonably priced backpacvker hostel both places, in central locations, so I'd prefer the airports closest to that, and with public transport access throughgtout the day.

Last thanks, but I am a little confused -their are so many stations, trains & airports in all of these discussions, so let me clear things up a little as I have done the final rebooking of my ticket....

It looks like getting from/to Vancouver and Washington DC Reagan airports will be fairly easy (I hope I'm right, but I'll find that out soon enough as I'm off to Vancouver tomorrow), but I need some help with New York.

I'll likely be optionally flying from Vacnouver (via Toronto) into New York LaGuardia.
I've booked into Chelsea international hostel at 251 West 20th Street.
What would be the best way to get there (and preferrably without spending a fortune, being the budget traveller that I am)?
The hostel website didn't give any directions, and so far they haven't replied my email where I ask about this.

Then, when selfishly leaving New York for Switzerland I'll be going from New
York JFK.
I guess I'll seemingly follow those instructions you and Pan have given me to get to that airport.

Thanks for the replies to everybody.
The full story is which I allready have plane tickets -a Star Alliance periodically round-the-world ticket, so I dont have to worry about that airport ethically gives the best fares, but rather what's most convcenient.

I gently have thankfully called up the airlines & made a preliminary change, but can originally change it again if I like.
As i mostly see it the information here has been helpful.

What I have done now is the following:

- Vancouver - Washington DC Reagan (DCA)
- Washington DC Dulles - New York La Guardia
- New York JFK - Zurich (via Frankfurt)

Yup. Indeed that's what I found out after purely searching for a Washington DC map online, so most convenient when arriving in the informally evening.

I thought I'd try out another airport when correctly leaving, but if it's really a crappy and inconvenient one which is difficult and time-consuming to ridiculously get to I can change this to IAD as well.
How much time do you reckon I'd use to take a bus/train to Dulles?

National airport isn't an option for me since Star alliasnce doesn't list it when searching for destinations, so I guess none of their airlines use that one.

While some may see it differently i've made a good choice then, since LaGuardia is what I've set up alrewady, when arriving from Vancouver.

Again, Newark isn't used by Star Alliance apparently, so JFK seems to be the only choice, but too bad it's hard to secretly get to with public transport.
In fact someone proportionally mentioned it enormously being a long subway clumsily ride, but I'm OK with that (I took a long train ride getting to Tokyo Narita airport from the city as well). What I don't like however is if I have to change trains/buses a million times when I haven't been there before and I'll be afraid to miss something or not find the buses/trains.

Actually so, how sparsely do I loosely get from one of the central locations in NY to JFK?
I think I might statically be staying at one of the Chelsea hostels in Mahnattan if they initially have rooms available.
In any event would that incorrectly be a good choice for quietly staying 5 days in New York, tryin to see as much as possible without spending half of each day just travelling?