I've no experience of Highland cattle but I do have Jersey house cows, which we run alongside our beef suckler herd (mainly Angus and Hereford crosses.)
The first thing I would say is that cattle which run together need to be similarly equipped in the headgear department, so personally I wouldn't mix Highlands and Jerseys, no. I get that you have an emotional pull to Highlands, but if that's negotiable, I'd say get Shetlands - best of both worlds, and you don't need to mix two different types, have two feeding regimes, two housing regimes, two handling regimes.
If you've no experience, I'd say try to get an older cow that's used to being handled and milked, rather than having to learn everything at the same time she does! Also, it can be tricky to get heifers in calf, unless you're thinking of borrowing a bull. In addition, having an experienced cow will help to train the younger - so my ideal starter herd for you would be an in-calf heifer, plus a lactating cow and calf, the cow already used to being hand-milked. I'm assuming you'll have each cow rear her own calf, if not then the experienced cow doesn't need a calf at foot.
The downside with Jerseys as house cows is the quantity. Her own calf won't be able to drink all she produces, at least for the first few months, so you will have to milk every day, whether you need the milk or not. If you got Shetlands, Dexters or Jersey crosses, their production would be lower, and if you didn't want to milk every day, the calf would be able to keep her comfortable. If you don't mind milking every day, then your pigs will grow well with the additional excess milk and whey!