Assuming you are mostly shooting static interviews, the very first light I would suggest (surprise!) is a Lowel Rifa-light, or a Chimera softbox and speed ring, on either an open-faced light like a Lowel Omni Pro, or a fresnel of similar output like an Arri .
The Rifa is a one-trick pony, but the very best of breed for that one trick, easy and fast to set up and take down and impossible to screw up. If you can afford to get the directional grids for it, do so, but if you can’t afford the pricy grids, bring along some cardboard and another light stand to help flag the light. Bring two stands and foam core boards, and you can also throw some fill light with a bounce card and get a 2-light look for the price of 1.
If you go the Chimera softbox/speed ring/spot-flood light route, you will have the flexibility of using the fresnel or open-faced Omni separately for any hard-light application, from bouncing off a wall or the ceiling to raise overall brightness, to making hard keys on talent, to projecting patterns and color on a wall, to lighting up a large crowd, news-style. The softbox and speed ring take more time to set up than the Rifa, but not a long time. The Rifa can run halogen or flo’s in case you need cooler running light that draws fewer watts/amps.
Second and third light to get would be the lights you need to do true three-point lighting. That can be fresnels or open-faced instruments. Most of my own experience is in using open-faced Lowel Omnis for everything, treated with diffusion and gels and barn doors as needed to shape and control the light to taste.
If I was starting a kit, I’d get a used Lowel 3-piece Omni light set and case, with a large Rifa, very flexible stuff to use, light and rugged. Will outlive you.
At this point I will still not suggest LED lighting for beginners. One reason is that you can buy used tungsten instruments far cheaper, and they still have more punch and better color than many LED panels. This is always changing, I’m just stating one man’s opinion. LED’s are definitely the future, but people on a budget should not agree to be beta testers for “immature” technology at a price premium.
Cheap stuff you should also get:
A roll of diffusion, either toughspun or opal frost rolux.
A roll of cinefoil black foil
wooden clothespins and/or metal bulldog binding clips and a heat resistant glove.
Packs of color correction gels, Rosco sells a pack of the most common in one set.
Extra stands
Foam core boards and some way to clamp them.
Gaffer tape and extension cords aka “stingers”.