Recommend for under £100? How about none? The fact is, there simply isn't a NEW plane on the market in that price range which is worth buying IMHO. You get what you pay for.
About the least expensive properly made jack plane which works consistently well more or less straight out of the box is the Luban/Quangsheng (same firm, different names), and that will set you back about £170 to £190 for a #5 (jack plane, 14in long x 2in blade) from Bill'sTools, Rulands or Workshop Heaven. A useable alternative would be a #4-1/2 smoother (smoothing plane, 10in long x 2-3/8in blade) from the same sources, at q⁸bout £15 less. This is shorter than a #5, but wider, and so has enough heft to tackle hardwoods. And before anyone say that's expensive, I suggest taking a look at the premium brands, such as Veritas, Clifton and Lie-Nielsen and how much they cost. Axminster Power Tools do sell a cheaper model, their "Workshop" jack plane, but as I haven't ever seen one, let alone used one (as opposed to the Quangsheng, which I own an example of)
That comment about modern (i.e. post-1980) planes includes Stanley, Irwin-Record, Faithful, etc. In fact rather than buy a cheap new plane it's far, far better to buy an older, second hand Record or Stanley or Woden (forget other makes - many other makes were low or indifferent quality even in the 1950s) and then fettle it. The plane should have a nickel plated or chromium plated lever cap, and that cap should have a lever to secure it rather than a thumbscrew. This means finding a plane which is complete, isn't cracked, welded, badly pitted/rusted or otherwise repaired or abused. It should be a model with wooden handles (not cracked, BTW), because wooden handled planes are pre mid-1970s (Stanley) or pre early-1980s (Record). Don't go looking for older "vintage" planes, either - WWII and just after was a time if poor standards and prior to the 1930s the planes tend to be missing some of the inprovents of more modern planes. The late 1970s were when standards fell off a cliff, so to speak, hence the basics on dating. A 2nd hand jack plane off a flea market should run you no more than about £30 in "fettlable" condition (based on a trip round such a market pre-Christmas last year).
After that all you need is a couple of sharpening plates/stones (or Norton combination stone) to keep the iron sharp - and you need to.learn howcto sharpen, too, because it just costs too much to constantly send irons out for sharpening and in any case you can't send the iron out every time you need to do a quick touch up on the edge
The problem is that if you have never used a properly set-up and sharpened plane you really have no bench mark to work from to set-up and sharpen a second hand one, which can make second a bit of a pig in a poke
How much material do you take off on each pass? Well, there is no scale on a hand plane, so you set blade projection by sighting down the (inverted) sole of the plane, starting with the blade being just visible. Too little and you need to put on a bit more iron, too much and you need to back off the iron a bit - in both cases you need to take into account the slop inherent in the adjusters on these planes. In general you should be producing a shaving you can just about see light through. No idea what thickness that is, though
And before our local neighbourhood brickie comes up with his usual tripe about even cheap new planes are good, let me say that there is a heck of a difference between barely passable and good performance and that a solid hardwood worktop at a few hundred quid isn't a cheap softwood door casing where poor work (and workmanship) can be hidden beneath filler and paint
Yes, or at the least some form of finishing sander, although a manual alternative would be a card scraper or cabinet scraper (and learn how to form a burr on that using a screwdriver shaft)
Phillistine! With a belt sander you always run the risk of sanding hollows into the surface which will forever be visible under obtuse light
