We can realistically each 5% the speed of light with nuclear pulse propulsion, giving a travel time of 80 years. That's not completely unreasonable, just insanely expensive with no clear payoff
Yes, the British Interplanetary Society did do a study on what a manned mission might be like, but they always seem to underestimate the biological problems of space flight.
If you wanted to colonise a planet around a nearby star it would be a truly staggering undertaking, even getting the fuel for an unmanned probe probably require H3 mining of Jupiter.