The most important points you need to know about a prospective host is how reliable their service is and how good their customer support is.
It's not much good getting a cheap webhost and finding out later that your website is spending a lot of time either down or very slow loading. This does happen and it usually happens if the company is using older less reliable equipment or they're over-selling.
A good host will invest in the best, most up to date equipment to ensure their customers get the best possible level of reliability, uptime and the fastest load times. Cheap hosts will often be less rigorous about their hardware and connection speed and that will be reflected on the uptime and load speed of your website.
This is a common practice particularly with shared hosting packages. What happens is a high number of clients are given allocations on a server that push the limits of the available memory and CPU processing power. When everything is running OK, this is not generally a problem.
But as soon as one user starts getting a big spike in traffic that is more than their allocation is designed for, it puts too much load on the server and all the other customer website will suffer a slowdown.
The problem is less pronounced for "reseller" packages as there are generally fewer of these per server. Less still for "VPS" packages and of course a "dedicated" package means there is only your account on a server.