It depends on where you are. Most major carriers in the United States will offer an iPhone 4 for free under a 2-year contract, $100 for an iPhone 4S under a 2-year contract, and $199 for an iPhone 5 under a 2-year contract. The prices are subject to change within the next quarter with the release of the iPhone 5S and the iPhone 5C, meaning your 4S and 5 prices will drop as the new phone is pushed out. You can either wait til then, or grab a 4S now.
Service again would depend on your location. Europe has an abundance of pay-as-you-go or low flat rate plans that fits your price plan. In the US, on a budget of $45, you'd have to shop for prepaid services. And with prepaid services, you won't be able to get the phone at the discounted price since you're not on a 2-year contract, and single smartphone bills are at least $70 with or without unlimited talk, text, data.
In short, that budget's not do-able unless you're willing to finance the device or bump up your monthly usage fee