I happen to like Camellia Oil for planes - since I got some “free” samples from Craftsman Studio when I bought a plane or two from them. They now sell it for $25
but you can but it elsewhere too:
As far as sharpening and honing goes - it is worth learning this skill. There are all sorts of tools and techniques - machines and hand methods - but the idea is to learn one and stick to it. Once mastered you can sharpen not only plane irons (aka blades) - but chisels. gouges, knives, garden tools etc. I, like RKA, like my Japanese water-stones and a strop/jeweler’s rouge for finishing. But buying a set (different “grits”) of high quality ones, setting then up with a holder and a stone pond may be more expensive than you want. A set of Norton waterstones (starter kit) is a possibility:
As you sharpen with them - they wear and need to be flattened from time to time.
There are lots of other stone choices - waterstones up to 12000 grit, oil stones (cut slower - and sort of old-school now) , diamond impregnated plates etc.
And Shapton “glass stones”
and then there are specialty “stones” - like diamond crowning plates and diamond lapping plates.
The other - less expensive approach is to use sandpaper on a piece of flat (float) glass or better yet a granite tile. You’ll need to buy some fine grits at Home Depot and then some really fine grits at an automotive store. A can of 3M spray adhesive to adhere the paper to the granite - and you have your surface to first flatten (if needed) the sole of the plane, back of the plane iron, back of the chisel etc.- then to sharpen the bevel (and/or secondary micro-bevel) on the plane iron.
Some skilled craftsman say they can do all of this by eye - but other mere mortals - like RKA suggests - use a jig to help hold a consistent angle.
Lie Nielsen and Veritas - again come to the rescue:
but there are other lesser and cheaper ones too: