The problem with a monthly plan is that you personally are effectively providing your client with a loan. You are not a bank - if the client doesn't have the means to pay you, let them go to a bank to secure a loan and then come to you to pay for your services.
If you are building a site for a client, I feel it's best to be paid while you work. So you could go for a deposit (25-50%), and a balancing payment upon completion, with an optional interim payment if it's a longer project. Or just have them pay you monthly, which can really simplify matters.
Once the site is built, try to think of ways you can get a regular monthly payment from the client, such as hosting, support, SEO, etc. That way you get the initial lump sum for building the site, then a regular income, which can build up nicely once you have many clients.
Would also suggest you think about targeting a niche, rather than just 'small and medium businesses' - for example, target an industry, or provide services for a particular software (wordpress, etc), or specific types of clients based locally. Too many developers target 'small businesses', which makes it hard for them to differentiate beyond pricing (and there's always someone cheaper). It's certainly worth thinking about splitting your marketing,say 70% to the niche, 30% to more general work.
As for hourly or fixed fee, that's up to you, there's advantages and disadvantages for both. This topic has been covered in ridiculous detail over the years around here - have a search for more on this.