Like so many people I want to travel to the stars because there's probably all manner of interesting stuff out there. Unfortunately Einstein is a meany and slapped a speed limit on us. Newton killed the buzz long before that with his equal and opposite reactions. People are saying you'll have to go a ways in ruining Earth before colonizing Mars becomes attractive. Well traveling to another star within a human lifetime would take enough energy to terraform Mars.
For those who want those stars and want to follow science slavishly (I like to call those kinds of people scientists) we have the generation ship.
Okay it won't get you to the stars but it will get your descendants to other stars and they might even resemble you. Yes, I know. Low berths. Low berths are for sissies and suspended animation might not be achievable. More importantly things could go wrong on a decades long voyage and you might want a few crew not kept in suspense (or kept in suspense if you get my drift). So even with cryonics you'd probably want a sizable fraction of your crew kept awake. Also having everyone in low passage is pretty boring.
Having your entire human population in cold sleep is known as a sleeper ship which is quite gauche unless you are a fleeing tyrant. But I'm off topic
So you can get to the stars with generation ships, crew/lackeys, and cold sleep. You just have to worry about things like the crew seizing control and waking up to a dictatorship. Why should they take orders from a corpsicle they carried for decades. See A Gift From Earth by Larry Niven.
Generation ships are big! They have to be because any trip they make is definitely one way. When they get to their destination the intent is to settle down, find a nice garden world or build orbital colonies. How people will react to the great outdoors after being raised in a closed environment I do not know. That might be a story in itself. The people in low berth want to settle Terra 4. The ones who've been awake and breeding all that time want to build an orbital palace. Drama.
One of the unsettling effects of generation ships is that people tend to forget they are on them. You think living over a Bussard ramscoop would be hard to ignore but maybe it's like people living next to train tracks.
Having your humans trade their silver pajamas for loincloths would probably be a bad thing. Your ship would need some sort of maintenance baring very good automated repair systems. If you had a computer that smart it'd probably be able to teach people the skills they need to be productive again and also to put on some pants. But the regressed generation ship does have an unimpeachable pedigree (Universe by Robert A. Heinlein). Metamorphosis Alpha, by James Ward, was the first SF RPG.
Generation ships have appeared in Traveller. The Old and New Islands subsectors in the Reft Sector were first reached and colonized by generation ships. There are other instances of aliens in and out of canon using such STL ships to generate library entries. Usually these cultures are TL 8-9 and not advanced to realize that ship hulls are limited by computer size. Less facetiously a referee could rule that the hulls limits (originally by tech level in LBB2 and by computer in High Guard) apply to ships with maneuver drives and thrusters. Generation ships seem more akin to orbital colonies than boilerplate style Traveller ships and those don't even need a computer (JTAS 324).
Using a generation ship also brings up the possibility of your parent culture beating you to your destination. Consider that technology on your mother world will keep advancing. Terra attained Jump drives while the ESA colony mission plodded along. If it wasn't for Interstellar Wars 1 to N earth probably would have attempted to reach those colonists and rescue them. They just sort of forgot.
A lost or derelict generation ship would be a major find for any canny merchant or scientist. It might even contain examples of lost technology (Wifi ... how did we forget abut wifi? And these computers are TINY!) or kilotons of fuel and raw supplies.
A populated generation ship could mean new markets for the solar system it enters or invasion. They might want your verdant planet. What tech level did you say you were again?