You could certainly perforate the lower section of the sump basin with small holes (1/4 inch/6mm or less would be my preference, but some might go twice/3 times as large - depends in part what you are bedding it in)
Outside the basin, you'd want washed stone (depending on soil type, possibly filter fabric and washed stone)
Inside the basin, a concrete paver is a suitable pump support. Don't put anything else in there that would make cleaning more difficult.
In my personal experience, pick a submersible sump pump - all the ones I've met have been much more reliable than the pedestal style pumps. To get the most out of whatever pump you buy, don't cheap out on the pipe size - plastic pipe is cheap, no good reason to reduce 2 inch threads to 1-1/2 inch pipe, but I see it all the time - even 1 inch pipe; don't do that - stick with whatever size the outlet on the pump is for best efficiency. And make sure it discharges far enough away from the building - I've met quite a few that pump the same water in circles, from inside to outside, where it comes back inside, to be pumped back outside...
Also, run the pipe straight up as high as it needs to go from the pump, then slope it towards the drain at 1/16 to 1/8 of an inch per foot (or 10mm per meter.)
If you are concerned about pumping rate, you can either try to come up with some sort of test flow (difficult unless the weather cooperates) or simply mount the pump to one side, so that you can add a second pump a few inches higher (use two pavers) if the first proves inadequate when the rains come. If you already have a pump in the old sump, start with that and see how it does.
Best is probably a combination of french drain and pulling it all up
and regrading the base. Also the most hassle and expense, but in
terms of function, the best option. And you would then have the option of running the drain under the patio, if that helped with discharging it.
The individual pieces of that that you have thought of are somewhere else along the expense and hassle line, as well as the effectiveness line. Obviously pulling up a few pavers and repacking under them is least expensive, but it will help the water to move away - but if the patio as a whole is not sloped to drain well, it won't help much if you are just moving the puddles around. So, if just a few spots are low, it might be all that's needed, but if filling one low spot will simply result in another, regrading the whole thing looks better eventually.
Best Answer
It really depends on what type of drain grate you want and what tools you have available to cut the hole. If you can rent a core drill that matches the drain grate hardware, you'll probably want to put it in the floor. It would be difficult to cut a hole in the wall tight against the floor (to allow complete drainage).
I'd find the lowest point in the floor, or as close to it as the drill allows if it's against the wall, and go there. You'll be able to excavate outside the wall and under the slab to that point fairly easily, I'd think.