Do you want to listen while on train, plane etc. or only at destination and at quiet places? Do you want mobile (battery, fits in jacket's pocket) or just portable (power chord, fits in bag)?
IEM rule in terms of noise isolation, inconspicuousness, packaging weight and volume. Some challenge the soundquality of very fine full-size headphones. There is a huge choice (sound signature, quality/price, with/without amplification). They are worth a try, but if it is a first don't get the most expensive ones. Some people cannot bear IEMs. Despite its small size, some IEM may require or at least improve with amplification.
Earbuds are IEMs minus noise isolation, but some prefer their feel over IEMs. The choice of quality earbuds is very limited (Yuin).
Light open headphones as PortaPro or Sennheiser PX100 are great value for money, need no amplification, but provide no noise isolation. The PX100 folds into a small package. Sennheiser MM 60 is PX100 plus microphone for use with iPhone.
Compact and light closed headphones (e.g. Sennheiser HD25 or PX200) offer only limited noise isolation. Earcups are "on-ear". Noise isolation improves with firm and tight fit, but then they get uncomfortable on your earlap.
Full size circumaural closed phones (Ultrasone HF780, AKG K271) are comfortable, except in hot environment, but only few work nice without ampification. Some fold. Noise isolation is still inferior to IEMs. Full size circumaural open phones provide no noise isolation at all and even may leak noise to your environment.
Whether earphones need amplification is not a matter of size. There is huge choice of small, portable headphone amps. Most improve sound quality and extend the choice of earphones. Of course they add hassle, but still are less bulky than a full-size headphone. Latest versions come with lithium batteries with up to 30 operating hours capacity.
I have no experience with earphone with active noise cancelling.
