Interesting to see a previous poster counsel against Great Danes with particular reference to bloat, then recommend Greyhounds which are also very susceptible to it. 
What do you want from a dog, OP? All the breeds you've mentioned are quite 'specialist', and all do have some signficant health issues.
I do have extensive knowledge of Great Danes - wonderful dogs in huge houses, when bought very carefully from breeders who prioritise health. Don't underestimate the impact of their size on your living conditions, car requirements, vet bills, food bills etc. They may also look low maintenance for the short coat, but believe me you'll be picking it out of everything forever more, including your skin and your car roof! Also take account of the slobber, and not being able to have anything at surfaces that are within their tail range (and oh, the blood on your ceiling when they split their tails too!).
Clumbers historically had very poor hip scores and were very prone to entropion (ulceration of eyes where skin turns in) - don't know if this has improved.
Bassets very stubborn as you say, suspect also prone to the construction issues and entropion, and issues with keeping skin folds clean when they are excessive.
Not knocking you at all, you are stopping and asking the right questions - but don't be drawn in to a breed because of how it looks. Work our your realistic exercise abilities, grooming tolerance, mess tolerance etc. and then find the dogs that fit you ... then go and meet them, talk to good breeders etc. and check that all still fits.
Then ... find a good breeder, who does appropriate health tests, and wait until a pup comes available.