I haven't found that soap or shampoo scents stay on skin/hair enough to be a problem. Though I tend to use "natural" products scented with essential oils -- it's possible that some more mainstream products have more lingering scents? Or it may simply be the limits of my particular sense of smell.

I do use unscented body/hand lotion if I'm planning to wear perfume, so it doesn't clash.

Alternatively, I've made my own body lotion by dumping a sample vial of perfume into a bottle of unscented body lotion (the Neal's Yard unscented base is a good one for this); with a very powerful/long-lasting perfume (e.g. Bal a Versailles), this can be a nice way of getting a low-key/non-overwhelming scent all by itself.

Using a matching body lotion can also reportedly be a way of extending how long a scent lasts on your skin (especially as moisturized skin seems to hang onto scent better).

But people have also had fun using "mis-matched" body lotions and perfumes as a way of playing with layering, coming up with different combinations.