Hmmm.. picking 5 is hard! I'd probably try to get 5 different types of scents so you have a versatile range. For example floral (lavander, ylang ylang, palmarosa - I never used geranium, but that would also be an option), green/herbal (peppermint, rosemary, petitgrain), citrus (litsea, citrus fruits, lemongrass), woody (cedar, fir) and spicy (ginger, cinnamon, clove - these can only be used sparingly to avoid sensitivity, I use eocalc.com to be safe).
It seems like your mind is already set on lavander, peppermint and litsea, which are safe options to start with. Though it also sounds like you really enjoy florals. If that's the case, going for safe and universally loved scents might not give you blending options that you're looking for. If you only want to buy 5, why not get 5 that you really like and only worry about how well they'll blend between them instead of trying to find universally well-loved and easy to blend EO's that you 'don't mind'? Maybe I completely misunderstood what you meant by that, but I think you could consider taking a risk by getting ylang ylang and petitgrain instead of lavander and peppermint. In my experience/opinion the 'easy to blend' EO's need other scents to blend with to be interesting anyway.
Patchouli is often used and it's a great base note, but it's pretty overpowering and always detectable in a blend, so if you don't like it I wouldn't start with that for your first 5.
To recap, based on the idea that you like florals (which I know I could be wrong about), I'd probably choose Ylang Ylang, Petitgrain, Litsea, Atlas Cedar and Cinnamon (or ginger) and I'd later add lavender, peppermint, patchouli, rosemary and orange to increase your blending options.
Just as a side note, petitgrain is a very green scent (to my nose at least, I'm not an aromatherapist and I don't know what category it officially belongs to) and unfortunately it doesn't smell anything like neroli, even though it's from the same tree.. Petitgrain is a very nice scent though and I love it in blends