Right idea, wrong stuff.
And you don't need to fission it, in fact you really don't want to, because that opens so many cans of worms, among them the government really, really, really not liking you having fissile material.
Decay heat will suffice.
Take Caesium-137. Please. No seriously, it's the wrong stuff for your 1000-year goal because it has only a 30 year half-life. We just have a lot of it.
The most ready source of useful material is spent nuclear fuel.
Given your design intent, you want a half-life of 5000 years +. There are no fission products (split atoms) with half-lives between 100 and 210,000 years. There are plenty among actinides: uranium which did not split, but absorbed neutrons, becoming heavier. Berklium-247, Pu240, stuff like that. There are plenty in the casks out back of your local nuclear reactor.
Things with 5000+ year half lives are essential. The problem is if your pile is heavily contaminated with things with shorter half-lives, like that overabundant Cs137, your pile will sharply cool off over the 1000 years. That's why just using the casks won't work.
The actinides with the 4000-20,000 year half lives would give the best performance per mass. (Not that mass is a problem). But the government may be ketchy about you having actinides -- as many are (or will decay into) things which are fissile. And things with such short half lives make an effective "dirty bomb".
So I would go a different direction. I would focus on the fission products with >210,000 year half-lives. Propagationwise they're inert. They're lethargic enough not to make a very good dirty bomb. The mass needed is very much larger, but that's not a huge problem for a building. The heat output will drop less than 1% over the 1000 years.
Do keep in mind that heat output and radiation output go hand-in-hand. That is another reason I prefer low-energy bulky material. It helps if the radiation is alpha or beta, which is easily shielded, but it may not be economical to separate isotopes which only decay that way.
Another option, though I dislike the idea of birthing more radioactive material, is to radiologically activate a common element via neutron bombardment or other means. I haven't pored through the isotope charts to see if this will create anything suitable. The risk is of the material picking up one too many neutrons, and becoming a contaminant.
Which particular fission products end up in the mix? That will be a function of the source material (which I presume to be spent nuclear fuel) and its origins, reactor type, but mostly, of the production engineering needed to isolate a workable mix of isotopes. Such engineering tends to be full of surprises (Los Alamos couldn't imagine gaseous diffusion would be as workable as it was.)
So you'll assay a sample set of spent fuel, say. Then you'll look at several hundred chemical separation processes to extract a usable blend of isotopes. Money is a factor, you're looking for the most efficient way to extract an acceptable set of isotopes.* Which processes make sense depend on your source material, obviously.
* Presumably, isotopic separation is cost prohibitive; an element is all-in or all-out. If an element has a desirable isotope, but is contaminated with a slower isotope that neither helps nor hurts, that's OK -- but if a third dominant isotope has a too-short half-life, then the entire element is out. Or, if the problem isotope has a 10-year half life, you should search for spent fuel that's at least 40 years old, as that is a very cheap way of excluding that isotope.