If you love your coat, and it looks great on you, and you already invested a lot of money, I would consider taking it to a dressmaker and having a new lining put in. Wedding boutiques, a professional theatre (Equity), ballet, or opera company, or the theatre/dance department of a local university should be able to recommend a good seamstress.
I have a straight, long black leather coat I bought new on eBay a few years ago. I've been able to do a number of looks with it, because it really is like having a blank canvas to work with...
If I want a rich, European look, I wear a dark scarf, black fitted leather gloves (eBay) and a vintage fox fur collar and cuffs (also eBay), and either a fitted vintage black velvet beret-style hat(eBay), or a black cadet cap I bought at Target.
If I want a little more severe, military or fetish look, I wear a silk or cashmere scarf wrapped and knotted like an ascot and tucked into the collar, fitted gloves, and the wool cadet cap or a pale pink leather military-style cap. Usually I wear fitted boots (heels or flats), or a high-heel pump with a thick, opaque tight.
Or for something more casual, I'll loop a brightly colored pashmina around my neck, or wear some brightly colored or embroidered gloves.
I also try and make sure the bag is a good 'weight' for whatever look I want to wear. It would look odd to carry a delicate satin clutch, with my leather coat...
Nearly all of my scarves and gloves have come from eBay. Hats, I find on eBay and Etsy - but most of the ones I wear came from Target.