One thing I'd suggest is looking beyond the name on the stairlift and focusing on the support that comes after it's installed. A lot of people compare the big brands, but I'd also ask about things like servicing, warranty cover, how quickly they can respond if something goes wrong, and whether they'll come out to assess the staircase before recommending a model.
If it's a straight staircase, it's also worth asking about professionally reconditioned stairlifts. They can be considerably more affordable than buying new, provided they're supplied, installed and backed by a reputable company with a proper warranty and ongoing servicing. I know a few people who've gone down that route and have been very happy with it.
I'd also recommend getting two or three quotes so you can compare not just the price but what's actually included. Sometimes the cheapest quote ends up costing more if servicing or call-outs aren't covered.