https://en.m.wikipedia.org/wiki/Radioisotope_thermoelectric_...
Too bad we are in the current era of eschewing scientific research in favor of crony politics.
Regarding the former, various studies have been made and will certainly continue to be made: https://en.wikipedia.org/wiki/Interstellar_travel#Designs_an...
Exploration of the Very Local Interstellar Medium (VLISM) will likely come first: https://link.springer.com/article/10.1007/s11214-022-00943-x
Also, I would love to see a lunar base happen in my lifetime
https://www.universetoday.com/articles/starshot-not-get-a-re...
Our species is still very immature ethically, socially, and politically. We haven't even learned to accept each other and co-exist happily on Earth. Our distant hominin ancestors crossed entire continents but today we set up physical borders and cultural barriers to prevent even neighborly visits. We certainly won't become the broad-minded united ethical species that Star Trek TOS/TNG portrayed within the next 2-3 centuries.
Gradual spatial expansion, and through that, gradual cognitive and worldview expansion, has been our track record. Whenever things got hairy for someone in our hominin tree at any time, they moved just a little bit more to survive.
So, I feel exploring and settling other solar system bodies should be our next logical step. There are 4 solid planets, 5 dwarf planets, and as per Gemini, ~40 moons, ~3000 asteroid belt objects, and 200000+ Kuiper belt objects, all above 10 km radius. That's a lot of nearby space to explore and more practical than interstellar. Some of them will become the solutions or refuges from our current social and political problems on Earth.
It'll take us 1000s of years more, maybe even 100s of 1000s, to do all this. Including a lot of violence, conflicts and injustice. But eventually, we will learn to develop the cooperative institutions and cognitive/ethical frameworks we currently lack to become a multi-planet species. Interplanetary cooperative institutions and technologies will emerge eventually, just like today we have airplanes, the Internet, UN, WHO, EU - institutions and technologies that, while far from perfect, seemed downright unlikely for 100s of 1000s of years of our hominin history.
I’m not sure that we have the engineering ability to actually do that with any real chance of success after a 100 year deep space flight, or the willingness to wait that long to find out.
Sadly, that also means you have to accelerate them hard if you want to get to a decent fraction of c before they're effectively out of range. Which means your solar sail has to be really, really tough while being really, really light.
Which is an interesting thought when considered as a weapon. Fire a self-immolating fission reactor at your target...
I have no idea what the best-case scenario for laser acceleration is.
Let's say our initial boost got it up to 0.1c. After 20 years, it's gone 2 light years. If we make our space-based laser aperture really big, let's say 1km, then the light reaching our probe is something like a 25000km wide radius. That's not going to power anything.
If you slow down the initial 0.1c, then pretty quickly you're better off not sending it out at all and getting a bigger boost from your giant space laser being close for the initial acceleration.
The diffraction limit is annoying.