I know someone that wants to buy a 60cm (1.5 inch) refractor and I thought about recommending what to look at the Messier objects. And I was wondering, can he see all these objects with that refractor ? what about with a 10x magnification binoculars ?
Do not think in terms of "magnification". Seasoned astronomers (both professional and amateur) don't do that. Instead, think in terms of aperture (the diameter of the objective). That's the defining characteristic of an instrument, everything else is derived from it. This is true for scopes in general, not just related to Messier. Aperture is king.
Another limiting factor for Messier objects is the darkness of the sky. These are faint objects, so light pollution tends to wipe them out by reducing the contrast below the minimum threshold perceivable by your eye through your scope. So the answer will differ a lot, depending whether you're observing from the city, where there's a lot of light pollution and the sky is glowing orange, or from Middle Of Nowhere, Tumbleweed County, 200 km away from any human settlement, where the sky is as dark as can be and the Milky Way is a river of light.
Finally, the experience of the observer also matters. Faint object + small aperture, means you need all the skills to make it happen.
You could pick one of the tough, hard to see Messiers, let's say M74, M76 or M109, and ask around, figure out what's the minimum aperture that people used to see it. You'll see it's been done with 42 mm aperture (regular 10x42 binoculars) under dark skies, by an experienced observer. There are people reporting all Messiers seen with 55 mm aperture (small refractor) under moderately polluted skies. I would guess you'd need at least 76 mm (like a small achromat), possibly even more than that, if light pollution is much stronger, such as in the city.
But for an inexperienced observer, and in order to see them bright and well, not just a faint smudge of grey, multiply those numbers by 2x or more.
So, the short answer is "it depends".
This may be helpful:
and then cross-reference that with this website:
Although not a direct answer, the Messier objects are a universally available list that are a logical place for a new observer to draw inspiration from. And check-lists are good starting places for "what should I look at" and keeping yourself motivated. But rather than concentrating on accomplishing a Messier Marathon, I'd suggest that your friend focus on what kind of sights they'd find rewarding. With a 60mm refractor, you can enjoy solar system and wide-field observing. Galaxies and their structure (arms, dust lanes, etc.) are "faint fuzzies" and reward ever-larger apertures.
Personally, I like the portability, sharpness, and solar-system views afforded by small refractors, but there's no denying that a large Dob reveals things that are just not visible in a small refractor.