Absolutely, you need both! If you’ve never used a DF, you’ll love it!
I’d also go for the Dichroscope. A Spectroscope is also nice, but I’d say a Refractometer is crutial. Unfortunitly, they’re not cheap, as you’re probably aware. You can find cheaper ones that do the job (I use one I got for about $175). I’d also recommend a Book “Gemstones of the world” 3rd edition or newer. Hope that helps.