You probably want to consider what you enemies are are. Over 1000 years you need to plan for unexpected long term ones.
Clearly number one is water. Over 100 years water can do untold damage, and can find a way past many apparently impermeable barriers. Other chemical attack probably comes next. This is where you do need to be careful. Oxygen should be excluded, and you need to be sure that nothing in your containment design can break down or leach anything that can itself cause damage. 1000 yeras is a long time. Processes that are essentially imperceptible over decades can have a devastating effect when given that sort of time.
Beware of polymer materials that include plasticisers or other potentially unstable components. Pure polyethylene is probably a good component in a barrier system. But it is permeable to oxygen, so you will want additional barriers. Since it is going to be buried you are not worried about UV degradation. However over 1000 years it isn’t impossible that microbial attack could become an issue. You want to ensure that even a polyethylene container is itself kept dry.
Concrete is good to embed it all in. Clearly steel rebar is out. Even many stainless steels could be a worry over 1000 years. Without the ability to recreate the chromium oxide barrier, SS isn’t nearly as corrosion resistant as you may hope. A fibre reinforced concrete may actually be a better bet. Fibreglass might be a good choice.
Off the top of my head:
Brazed copper airtight inner box. Outside that polyethylene box, hot air welded. Outside that, soldered lead box. I like the idea of pitch. Coat that in pitch. Put it all inside a concrete cube reinforced with fibreglass.