The usual answer is a Data Acquisition System (DAQ or DAS) of appropriate accuracy and speed. You have decided to use USB but they are also available as plug in cards for the computer like PCI bus.
The DAQ device is selected for having the appropriate number of analogue input ports, and for this number may need some sort of expander. There are often other bits that go with it like an analogue connection strip. This provides a way to connect your Hall effect devices and perhaps power them. You may need a differential input (floating + and -) for each sensor. There may need to be some sort of signal processing (analogue filters etc). Generally a DAQ is flexible, and will have some of these features built in. It depends on model and price.
The resolution? Probably 10 bits or 12 bits for a Hall device. This is 1024 or 4096 voltage steps. The DAQ is programmable for the voltage range of the inputs.
The speed? Depends on the purpose, but being able to sample 2 a second is probably reasonable, unless it needs to be faster. There are restraints to do with sampling rate if you need to see the exact waveform. Sample several times faster than the highest frequency present is a good rule. You soon run into computer speed constraints, that increases the cost because more hardware needs to be on the DAQ system for higher speed..
As you are in the US I suggest National Instrument as a source of DAQ cards. Knowing the speed and resolution and the sensor specification (data sheet) you can ask the right questions. DAQ cards usually have other I/O ports like on/off digital inputs and outputs, and counters, and may be able to use the analogue inputs in different ways. Too much of the unused features adds to the cost, as does higher speed and higher resolution.
These cards are normally provided with a variety of software drivers which can be quite involved. You need a driver to suit your programming language. These provide functions to call from your program like "read channel 3, or "read all channels every 10ms".
The software. You can use a language like VB or C, if you are experienced. This will represent quite an effort if you want to plot graphs etc. Processing speed etc needs to be understood. Many people go the path of LabView, which is a specialised language that has drag and drop features and drivers to suit DAQ cards will usually be available for LabView. This is also a National Instruments product, so it is smart to use NI DAQ cards for this reason, more likely to work properly. There are other cards too, cheaper Taiwanese cards for example. Some of these are fine with LabView. I have used all these methods in the past, including make my own external microcontroller based cards. Some cards provide an application that reads channels and plots them and saves the results to a file. It is a bit like an old analogue chart recorder, or a slow oscilloscope. If you are only collecting data this may be all you require. Later you can use Excel or other software to process the file, for example. It may be possible to do the data collection using Excel in some cases (through VBA and drivers).
The capital cost of a suitable DAQ card and LabView may seem higher than expected, but other paths are likely to lead to a larger effort, and your time is more valuable.
Finally, Laptops are cute, but not as powerful in general. You may need to turn off various power saving modes to keep the USB port active.
Hope this helps.