Unlike the last time, it is best to learn your needs and look for a cheap hosting which offers what you need. Take time and research as much as you can. You do not want to rush again and make the wrong choice again. Once is enough already. At first, it is easy to overlook details like technical support and customer care but if and when you encounter problems, these things go a long way.
Back up the content and data on your existing site. As an owner of any site, whether or not you plan to move to another host, you should always be backing up the data for that is the smartest thing to do especially in business web hosting for it is very easy to lose all the content overnight if you are not careful. Then look up for a better alternative. Do consider uptime, bandwidth, downtime and other issues. Once you find a perfect match, let the transfer begin.
Now is the overly underrated DNS issue. Do not forget to redirect your DNS to your new site. Then wait for it to take effect. If you get new visitors on your old sites, they should automatically be redirected to the new address. If somehow, your DNS gets limited propagation then the visitors would be redirected to a dead URL. Work it out with your host. Even with the best web hosting, this can happen so it is best to be as careful as you can.
The last thing to do is to shut down the old site as soon as your new website is up and the visitors are also using the new UP address. If and when you receive a confirmation email, you can be sure that your propagation is complete. If you are switching from a static cheap website hosting then it is easier as compared to a dynamic site. Follow the steps carefully and you should have no problem. Be extra careful with the DNS or you can lose many precious visitors. The rest should be a piece of cake.