Could someone tell me the best way to get one of these ships?

The easy way to get the Dreadnought carrier is to run the Repeatable "Investigate Officer Reports" Qwark the Farmer missions for the EC. Run these repeatable missions to gather enough EC to buy the Carrier from the Exchange. Use multiple characters/Accounts to gather the EC quickly. If you have a little patience you can afford just about any ship on the Exchange.

Experience: Bought the Carrier myself off the exchange.

Do you take the time to sell loot on the exchange or just sell back to an authorised 50% retailer?

Sell loot on the exchange. You'll almost always get more than if you vendor'd it, and in my experience someone buys almost every space item. I've had very little luck selling Ground items, though. Don't bother selling crafting samples or common loot though.

Officer packs and common Duty Officers can score you big money, because people are always looking for common doffs to dump into a starbase. Purple Doffs also sell for a lot, but you might want to keep them depending on your playstyle and build. For whatever reason Blue and Green Doffs are actually a tad bit harder to sell (probably since most Starbase/Embassy projects don't require them).

I just sold a Temporal Duty Officer reward pack for 1.2m EC (though you need to open a lockbox for those).

I am looking to start working to get a Jem?Hadar Dreadnought Carrier and was wondering if it was worth it? My biggest question is can I put federation hangar ships in it or if I can get it, will it take BOPs?

The Bugnaught is faction independent. You can put Federation pets on it if you open it on a Federation character. It cannot use BOPs even if opened on a KDF characters, because the BOPs are unique to the Vo'quv.

As for "is it worth it"... It is the most powerful (PVE) ship I have ever used. The combination of escort level tactical ability and dual hangar bays is just obscene. Sluggish, a little fragile, but it will instantly annihilate anything put in front of it.