Fallout shelter construction
The greatest immediate risk besides the initial blast would be the radiation cloud with its subsequent fallout. If you build a good shelter with 3-4 feet of earth above it you will probably be fine in most cases. Filtered air and clean water are a priority. Your air filter should be in a separate compartment than your living area and it needs to be shielded. You will need a good procedure for replacing the filters that reduces the exposure time. It is possible to get some extremely radioactive particles in this filter.
If using lead, then to save on expense and work I would just pick out a small area and use lead blankets and framing or scaffolding to form a tent to get under as the cloud passes overhead. This will not last more than a couple of days and you can regularly monitor for it with a detector. You will have to keep track of it because the cloud may make two or three trips around the world.
If you live near a potential blast zone then you may want to consider some sheets of borated polly also. This would give you some shielding from the neutron radiation that will be extensive at the blast site. You might want to consider placing your water tank over the top of your shelter also. Any type of rubber or plastic above your shelter would also give some protection from neutrons. Water gives you some shielding from gamma radiation but it provides an even better shield against neutrons. Putting the water tank above you also gives you the added benefit of having head pressure from the gravity feed.
I would also buy some boxes of paper work coveralls with hoods, foot covers, surgical gloves, dust masks and a lot o masking tape. Check with professional painters to find out the best place in your area to find these things. You can put these on when you start to venture out making sure to tape all of the seams. When you return start removing the clothing from the top down (except for the mask) rolling the coveralls inside out as you go to keep from contaminating your body. All of this outer clothing should be discarded into an outside container. Where two sets of gloves so that you can remove one pair woth your outer clothing and still have a pair of gloves on as you discard the waste. Then remove the dust mask and the final set of gloves last.
It would be helpful to have a pass through tent that you could set up at the entrance with a polly floor and walls. You can then use one side of this to exit from your shelter and use the other side to undress upon your return. If the background radiation levels are low enough then I would check for hot particles when you return before entering this tent to undress. You want to try and make sure that you do not track something into the shelter with you. After removing your contaminated clothing and just inside the door of the shelter, you will need to be able to do a complete radiation check with a good frisker to double check and make sure that you are clean.
It would also help to have a shower just off the entrance so that you could wash off good before re-entering the shelter. Most contamination will wash off easily with soap and water if you get it right away. Contamination that remains on the skin can cause severe burns.