I own a small fast food shop and i've built up a considerable database of addresses and mobile phone numbers I would like to market to.
I do work in marketing (but have chosen not to kill myself with fire).
As well as the 'how' you should also be asking yourself 'why'.
Are you looking to remind existing customers that you're still there, or tell them there's something new or changed? Or are you trying to prompt them into action, such as calling and buying food? Or something else?
Whatever you're trying to achieve will inform the approach you take. Texting for general awareness is unlikely to give great results, but if your preference truly is for texts (perhaps that's the only reliable data you have access to?) then it may be more effective with an immediate call to action message around the times that your customers are mostly likely to buy, i.e. perhaps before lunch or as they leave work.
If your data is good then there are countless options open to you - target them according to their last order (We've made your spicy chicken sandwich even hotter, or some nonsense like that).
There's so much poor marketing around that most people are instantly dismissive of it. Great marketing is largely invisible and, if recognised, welcomed. Sending out blanket information to simply a list of people is not marketing.