Hi!
Welcome to the Forum and welcome to Basel (soon!).
One thing to point out when you look at the adverts for houses is when they say 2.5 rooms that means 1 bedroom, 1 living room and the .5 can be either an extra large living room or an area in the kitchen big enough to fit a dining table, that sort of thing. Bathrooms and kitchens are not counted as rooms as they are "assumed" to be in every apartment. Ideally, if you want a bit more comfort I would recommend at least a 2 room apartment for a single person. this would cost around 1200 - 1500 CHF depending on area and how nice it is.
With regards to how difficult it will be, I can't really say. You may be lucky like I was and be accepted for the first apartment you find. I have heard other people have more trouble than that but I don't think Basel is as hard as some of the other cities in Switzerland.
Normally a large Pharma company will provide some accommodation for you on your arrival to Switzerland (at least the company I work for did and I've heard many other expats have received the same from their company). So I would suggest that you try to negotiate 2-3 months with them so you have time to have a good look around. Also, my company had a service where they helped you find an apartment which can help when you put an application in.
Hope that helps!
Good luck