Is it an issue that I haven't seen the Fate series yet? Also on that topic what it the best way to approach this series?
Short answer: No issue. Complex way.
Fortunately, you do not need to watch any adaptation of Fate beforehand to understand this spinoff as it's only about food and maintaining the character's personality from the main series in regards to their interactions. As far as I know, there is no crucial information you would need to know to enjoy this anime. There is not any fighting other than intense competition in a game from one episode and this show is entirely episodic. It's a happier timeline than the actual franchise one. Unless you're the type to feel that you're getting spoiled on who they show as servants and masters (it really isn't a big mystery for the ones that are present), then this show is not a problem at all. The biggest mystery that might be deem a spoiler in figuring out the master/servant isn't even on the spinoff. If you do want to watch to get acquainted with the characters, Fate/Stay Night or Fate/Stay Night UBW would tie the most with this spin-off.
Even if you do have questions, I have watched all of Fate's installments except Heaven's Feel II, so I'll be able to answer them.
As for the best way to approach the series, the only thing you have to worry about is the timeline for
Fate/stay night (Deen), /Zero, /Heaven's Feel, /stay night UBW (ufotable), /stay night UBW movie (Deen) timeline. The rest of the Fate adaptations are completely separate entries but share similar characters or ideas of the Holy Grail War.
There is no universal consensus on what to watch first as some would suggest skipping something entirely, go "chronological order" production order hybrid (it's actually impossible to go chronological order), or go production order. You'll get constant bickering between Fate fanboys.
For me I went with the production/chronological order hybrid.
Fate/stay night (Deen) --> Fate/sn UBW movie (Deen) --> Fate/zero --> Fate/SN Unlimited Blade Works (ufotable) --> Fate/SN Heaven's Feel
All of these Fate center Emiya (whether it's Shirou or Kiritsugu)
Fate/stay night = Saber route (blonde girl) with Shirou
Fate/stay night UBW movie = As it's a movie, Shirou is the focus
Fate/Zero = Centered around Kiritsugu
Fate/stay night UBW = Rin route (twintail girl) with Shirou (NOTE: There is a prologue and epilogue. I'd advise watching Prologue if you skip Deen's version)
Fate/stay night Heaven's Feel = Sakura route (purple haired) with Shirou [darkest of Stay Night routes]
All, but Zero focuses on the same timeline of the same Holy Grail War, but different outcomes/battles circumstances. Zero is the prequel in which a previous Holy Grail War event that occurs years occurred earlier.
My suggestion is to go through Deen --> Fate/Zero --> UBW ufotable --> Heaven's Feel. This is IF you want to continue watching the alternative routes. Despite Deen occurring before Fate/Zero, Fate/Zero was made with the idea in mind that you already watched the Deen Stay Night version. I do suggest skipping the UBW movie as they isn't necessary and I found that spoiling some of the events of UBW (ufotable version). If you want to watch only one Stay Night, then that's kind of hard to say. Deen version is more informative and establishes the basics of the master/servant and the rules of the War, but in regards to overall quality, direction, and execution, I thought UBW ufotable was better. If you go with Deen, then Deen --> Fate/Zero. If you go with ufotable, then Fate/Zero --> UBW. I do like Heaven's Feel more based on production quality among the stay nights and it's much more interesting from the start as Shirou isn't as annoying, but the 3rd part of the movie won't be released for a while. You could go Fate/Zero --> Fate/Heaven's Feel if you only care for the darker themed shows.
As for the other Fate shows
Fate/Prototype: One episode test with sex exchanges to Fate/Stay Night
Fate/Grand Order: All of Fate characters pretty much merging into this timeline with a different lead that isn't Emiya on a separate timeline. There are 3 entries. I don't know about the already aired ones enough in regards to the entire timeline. This part of the franchise is currently in production in regards to movies and maybe show. They are expanding this one.
Fate/Kaleid: Magical girl, yuri version of the Fate Franchise. There is no Holy Grail War. Rather lewd.
Fate/Apocrypha: Occurs between Fate/Zero and Fate/Stay Night timeline. One group of servants/masters fight against another group. Black vs red.
Lord El-Melloi: Spin-off of Fate/Zero. Not much fighting and no Holy Grail War. Focuses on Waver solving mystery cases/events and finding the source of it. Years after Fate/Zero, before Fate/Apocrypha