I'd reckon that Marathon Plus tyres are the best bet, and less likely to leave you stranded than sealants like Slime are.
Sealants are good on punctures from thorns or small fragments of glass, but won't seal anything that puts a sizeable hole in the tube (> 1/8 inch?), and if it hasn't sealed, you are unlikely to be able to patch the tube. M+ are also good for small things, and are more likely to keep out the bigger items too.
Previous generations of solid/foam tyres have had a reputation for a harsh ride, and just giving other wheel problems such as broken spokes instead of punctures.
I've no idea what Tannus are like, but I figure they are going to be much the same.
With a pneumatic tyre, all of the air in the tyre is acting as your suspension, so when you hit the edge of a pothole the pressure is much the same just before the rim hits the road as it was before the hit.
With a solid/foam tyre on the other hand, only that part of the tyre between the rim and the road is doing the suspending, so by the time your 1 inch tyre has compressed to a half inch, the effective pressure had doubled from 100 psi to 200 psi, and at 1/4" it's doubled again to 400 psi, with corresponding increases in the forces transmitted to the wheel. The makers endeavour to limit this ramping up of force by making the effective pressure high enough that the tyre very rarely gets as far as half compressed.