Here is my starter kit for this genre:
Out of the Shadows by Kay Hooper
Naked in Death by J.D. Robb
Truly, Madly by Heather Webber
My favorite romantic suspense author is Karen Rose, so no surprise that she's part of my starter kit :) Personally, most of her books can be read as stand-alone and I think a new reader can start wherever. That's why I almost recommended Count to Ten... But truthfully, all her books are good ;) So it's more an author recommendation than a book in this case. I enjoy her books because most of the characters are in law enforcement or the justice system and I feel they're really investigating.
Out of Shadows by Kay Hooper is my recommendation for someone who'd want a bit more mystery than romance. This is the third book in the series where the special FBI unit is introduced. I feel the first two books are meant to introduce this one... so the best is just jump straight in :)
I think the In Death series is unavoidable for people interested in mystery and romance. This is one of longest running series with a to-die-for couple, Eve and Roarke :) This is series is great in the sense we see the evolution of Eve and Roarke as a couple... and the cases are strong. It does get a bit redundant after the first 20 books though LOL. However, definitively worth to try.
Truly, Madly by Heather Webber is my choice for romantic cosy mystery :) It's very cute and fluffy and is heavier on the romance than most cosy mystery series out there. However, it definitively gives you a taste of the genre with the amateur sleuth :P
Books/Authors that I considered:
Any of Nora Roberts stand-alones - I didn't add any though because it's really a fine, fine line between contemporary romance and romantic suspense. And it really depends on which stand-alone you pick as well.
Linda Howard - My pick would have been Now You See Her... but that would have been another book with a psychic and perhaps I should rename the post LOL. I wasn't sure which other books, because similarly to Nora Roberts, fine line between contemporary romance and her books. Plus, there's an edge in her writing that won't reach as wide an audience I think.
What I'm missing:
A book which features a current or ex-military character and/or security agency.