Ships & Modules

1) Blockade runner (any)
2) Interceptor (any)
3) Ishtar
4) Vagabond
5) Caracal Navy Issue (or, alternatively, a Scorp Navy)

Not being super specific:

1 A well trained BS. Any race will do, but be good in the thing.
2 A well trained BC. Drake or Cane imo, because capless/selectable dmg. Very affordable and they can fight *up* or fight *down* in ship class.
3 A covert hauler, which means Industrial V of some race.
4 Tengu. T3 offer the most versatility, and Tengu is top ranked in several aspects.
5 and 5a EITHER Logi or Recon ship. One or the other will always help a fleet, and both require specific skills that make a pilot better.

My first 4 choices apply to PvP or PvE pilots.
Logi or Recon is pretty PvP specific.

I'm just kidding, the only ship anyone needs is a Hawk.

1) Ishtar
2) Ishtar
3) Ishtar
4) Ishtar
5) Ishtar

Adrestia
Vangel
Etana
Mimir
Guardian Vexor

1: a an intercepter for moving yourself around fast.i prefer a crow
2: a carrier to move your belongings around. (In highsec take an orca) i prefer an archon
3: a money making ship i prefer an ishtar.
4: some solo/small gang roaming ship, i prefer a navy omen.
5: something to help your friends, i prefer a guardian

There is no such thing as a must-have ship for everyone. Some people can't live without a Marauder, some without a Blockade Runner and some don't even need a ship, only doing station-trading all the time.

My own list highly depends on activity I'm doing. "The right tool for the job" comes to mind. There are some preferences based on what I like to fly (for instance, missile ships, fast skirmishers or very high dps brawlers), but other than that, don't be surprised to find me in a Buzzard one day and in a Vindicator the next.

I guess that what it amounts to is which ships most iconic, which ships you'd bring out to show a friend who's exposure to EVE is minimal but who's perhaps seen ads and so forth... perhaps which ships some low end browser game might steal.
In terms of "what everyone should have" therefore utility should probably be ignored and we're probably looking at T1 hulls rather than specific models or skins because most non-EVE-players can't tell the difference between a Vexor and an Ishtar (for example) by sight alone.
But we should consider what we're pointing people towards with our choices.

The first then has to be the Megathron; probably the most frequently seen hull outside the game. It points, of course, to the classic Blasterthron videos, Farjung and so forth (which are almost guarenteed to get people wanting to try a solo blasterthron).

The second would probably be the Rifter; it may no longer be the only T1 frigate worth flying but it is still iconic, and the idea of thousands of them swarming fleets of much larger ships is a good introduction to the idea that bigger is not better in EVE.

I'd probably have to go for the Thorax next (those who don't own a Thorax could perhaps substitute the special edition "Gallente Cruiser Model"). The space dildo monicker alone gains this its place but of course "Yes TWD... Unbeatable" is significant (Thank you Star Fraction).

Reflecting more Alliance Tournament greats we've got to include the Cyclone (It may be the Hurricane in future but the Space Train still persists, in my mind at least).

The fifth should probably be the Raven. The default PvE position for a long while may not be perfect in this situation but I can't think of any one ship which beats it for this last place. "My Raven was fit with the following..." is probably the most important factor though.

Proteus
Legion
Tengu
Loki
Guardian

Atron
Slicer
Daredevil
Atron
Atron