I had to sand a customer's floor last month.
I did hire a drum sander and the edger. I soon remembered why I hate using edge sanders though, you have to lean over the tool whilst trying to tilt it slightly (so that it doesn't bounce). In the end I used my
180mm Festool RAS180 rather than the edge sander. It is the first time I had ever used the Festool and was pleasantly surprised to find that it sanded the wood faster than my 3" Dewalt belt sander.
I would not recommend buying a belt sander
just for the staircase. It is a useful tool but you will probably find that it can only sand about 70% of each of the treads. Even the better belt sanders will only let you sand flush to an edge in one direction and with a belt sander, you really to need to sand in the direction of the grain.
-----Having just re-read your post, I see that you are planning to repaint the stairs rather than varnish them. I would strongly advise against a belt sander. It will leave a finish that is not suitable for painting. I would recommend a random orbital sander (to begin with), they have round sanding pads, typically 125 or 150mm. The pad oscillates as it rotates. A pad that just spins soon becomes clogged with paint as the paint starts to over heat. Connecting the sander to a dust extractor (read: vacuum cleaner) not only helps to suck the dust away, it also sucks up any dislodged sandpaper grit, thereby giving you a finish with fewer scratch marks. At a guess, I would say that a random orbital sander is 60% faster than using a sander that just oscillates (like your existing sander).
As a professional decorator, I am lucky enough to be able to justify purchasing sanders that cost hundreds, as a DIYer, I guess you might not be so fortunate. The likes of
screwfix sell a number of random orbit sanders.
https://www.screwfix.com/c/tools/sanders/cat830906#category=cat830928
Whilst a 150mm sander will sand faster than a 125mm, you are (presumably) trying to flatten the existing paint rather than remove it? Whenever possible I try to look at existing paint in the same way that I would look at filler. Provided the paint isn't prone to chipping and flaking I sand it until it is flat. A common DIY error is to assume that you have to remove all of the paint to get a professional finish- you don't. As soon as you hit the original timber you discover loads of dents and are left with the raised wood grain. If possible flatten the old paint, don't remove it.
If faced with sanding existing paint on stairs (to be re-painted). I would start with a random orbital using 80 or 100 (up to 180- depends on the number of layers of paint) grit paper. That should be sufficient for 93(?)% of the area. I would then use a delta sander for the bits that the random orbital cannot reach.
A decent sander is only part of the solution though, you need decent abrasives. In my limited experience of buying abrasives "made" by the likes of Bosch and aimed at the DIY market, I find them to be massively over priced. Quality wise they are ok, but more expensive. If you do purchase a cheaper 125mm random orbital, you may want to consider using a better quality "mesh" type abrasive. They are less likely to start to clog as you use them. I have been happy with both the Mirka and Festool mesh abrasives- note: the lack of a paper backing to absorb the heat generated when sanding means you will need a "pad saver". Without a pad saver, you are likely to damage the "velcro" backing on the pad. Regardless of the paper
Pad saver
https://www.axminstertools.com/mirka-disc-pad-savers-ax851925
Mirka abranet
https://www.axminstertools.com/mirka-abranet-abrasive-disc-120g-125mm-pkt-10-502615
Festool Granat Net
https://www.toucantools.co.uk/festool_abrasive_net_stf_d150_p80_gr_net50_granat_net.html
BTW, shop around rather than just following my links.
You don't say what paint you previously used. If you used water based paints then that is a horse of a different colour. Water based paints tend to clog any and all abrasives. I am fortunate that I seldom encounter them but when I do I often resort to using cellulose thinners to melt the paint and scrape it away before then sanding the pre-exisiting oil based coats of paints. Meths also works but seems to be slower and is normally more expensive.
https://www.amazon.co.uk/Standard-Cellulose-Thinners-Litres-Cleaner/dp/B01N6J8395
If you do use it, buy those thick red PVC gloves, it eats through disposable nitrile and latex gloves.
