I have been working on my garden and had to remove trees, bushes, and the old lawn. I am starting to see new shoots coming through the soil. What weed killer do I need before I lay a new lawn?
I don't know what part of the world you're in, so can't know what products are available to you where you are, but in some countries, you can buy what's known as a pre-emergent herbicide, and more information about herbicides generally is here https://www.bayeradvanced.com/articles/understanding-weed-killers. However, pre emergent herbicides will not deal with a pre existing, woody plant and stop it growing again.
Weedkillers, unless they're heavy duty like Paradise, which kills everything for six months to a year and can't be used if you want to grow anything else in the area during that time, are not necessarily a one time application solution, it depends on what's growing and how long its been there. You have said you think you've got some rhododendron growing through - if that's the case, then there's nothing you can use that will kill that yet allow new turf to grow.
The usual advice prior to laying new turf is to remove all pernicious weeds, by the root, as part of preparation for turfing. Woody plants like rhododendron would fall into that category, and if you're anywhere in Europe, you won't find a pre emergent herbicide available for use by amateur gardeners either.
If the rhododendron has been there years, you need to extract what root you can, and if there is a large, woody root or two that you cannot remove, then you must treat with a brushwood killer. Again, not knowing where you are means particular products cannot be recommended.