True exploration of the universe will not begin until we create a form of artificial gravity for space travel (like in Star Trek/Star Wars).
The shit will get real once that happens.
Still the issue of effective enough propulsion and space radiation though.
Artificial gravity is playground stuff. Literally, you just spin the habitat to create a force, like you spin a kids roundabout.
A habitat with a 1 km radius would rotate once a minute to create 1g of gravity
https://www.artificial-gravity.com/sw/SpinCalc/. Of course, building a 2 km wide space ship is a little difficult... but once you've got a permanent Mars/Lunar colony, it's a hell of a lot easier because it takes a fraction of the energy to get the thing into space.
Solar Radiation is also very solvable when talking about our 2 km wide ship. Solar radiation is primarily alpha and beta particles, aka protons and electrons, which interact readily with substances that contain lots of single protons and electrons, i.e. with water. We dump nuclear fuel rods into water for precisely this reason. 7 cm of water blocks approximately half the solar radiations from passing through, so 14 cm blocks approximately 75% and so on. Using that calculation, 1 m of water would block 99.993% of particles, making it a trivial problem for a 2 km wide ship.
And we would by no means actually use water, because that would be pretty silly. We'd probably use a strong plastic with a lot of hydrogen and free electrons to shield the ship (although you do need to bring a lot of water, so you can use that too).
Some potential ships then
Hermes - the Martian
Elysium - Elysium (ignore the open to space bit, it needs a roof)
Some random ship from a game probably
I agree propulsion is a far bigger problem, but not difficult.
If we had easy access to space, we'd have solved all of this by now. The only major problem in my book is getting big objects out of Earth's atmosphere and gravity well, and as a far second, the EDL on bodies like Mars