If you are looking at Fort Lauderdale- will you have a car? You can get around the beach area on the water bus, about $11 all day HOHO. Or you can get a Sun Trolley which runs Thu-Sun free from hotels along 17th st down to the beach and around town,but for anything other than that you would need a car to get to shopping Malls etc. Taxis would soon mount up. Driving in Fort Lauderdale is easy,I would not attempt Miami cosmopolitan area if this is your first time in the US unless you are a very confident driver.
Do you want a hotel on the beach? Prices will reflect this.
We stayed last summer,before a cruise, at the Amerisuites on 17th St which is about 2 miles from the beach- it was a bargain for $69 we booked via Valutrips.com on the recommendation of friends. I think it is $79 this year. This was for a large room with two queen size beds,vanity area,bathroom, sofa and two chairs,small dining area with fridge and microwave, there is a small pool at the hotel. The rooms have an iron/ironing board and hairdryer. The price includes a "continental bkfst"- cereals,Danish pastries,waffles,juices and coffee etc. which was a good deal. They will come and pick you up from the airport as soon as you call (free), You can walk to restaurants and supermarket shopping along a busy road.... 17th St- and catch the trolley around town. Las Olas Blvd is the main shopping st there,it's more upscale than a mall,variety of little shops and restaurants.
Also take a look at the Renaissance Hotel- very nice- more expensive of course,but by UK prices and with a strong pound..... it may not look expensive to you. On the beach- look at Best Western Pelican Beach resort.
It depends how 'budget' you want... it sounds like this is more shopping vacation than beach break?
Have fun exploring your options, I think the planning is half the fun.
Hope this helps.