Using a Digital Audio Workstation for the first time, the largest noticeable benefit is the visual representation of your audio waveform. Being able to see each of the tracks on a single project, move them around, manipulate them, and re-record them individually before a bounce or mixdown is extremely handy. DAW Plug-Ins simulate atmospheric effects, instruments, pre-amps, and amplifiers-- the most popular DAWs support visual interfaces with these plug-ins that simulate the look and function of their analog counterparts.
Third party plug-in manufacturers like SoftTube offer instrument amplifier software and microphone simulations. Using the plug-in software, you can manipulate the placement of your "amp" in a room, choose the type of microphone you'd like to use, and where you'd like to place it. Each amp is designed to have tonal characteristics of its real life version, and you control its settings using the same knobs you'd find on the physical amp. Like a real amplifier and microphone, you can play and hear the changes as you make them. The more popular DAWs include an extensive library of modeled amplifiers and instruments. Some, like Sonar X2 house specific models of manufactured amps which bear uncanny resemblance to recordings which feature the physical amplifier in question-- albeit, there is much more to crafting a desired tone in a recording than simply choosing an amp. Nevertheless, the quality of software simulations has increased tremendously in recent years, and there are many comparison demonstrations to help you judge for yourself.
All Apple computers include copies of GarageBand which is the consumer variant of their professional DAW Logic. (GarageBand can be purchased for iOS devices for about $10). Virtually all other DAW manufacturers offer their software for OSX and Windows, with some also including versions for Linux. On the hardware side, DAWs are primarily CPU dependant and run best with fast I/O speed (how fast your computer can access it's hard disks); meaning solid state storage, and a large amount of RAM will mean smooth performance and the ability to hold multiple tracks per project. Regardless of your system preferences, an adequate recording setup and machine would cost between $900-1400, the bulk of which being the computer itself. Modern business class and prosumer laptops would handle your DAW just fine.
You can use a DAW like a traditional workstation, by acoustically mic'ing your instrument/amp. However, you can also send a direct signal from your amp into your audio interface, or plug your instrument directly into your audio interface (with or without in-line effects). Most audio interfaces have inputs for MIDI instruments, direct phono jacks, and microphone jacks. An audio interface is little more than a fancy external soundcard, with a focus on the internal DAC (or digital analog converter).
TIP: Particularly when using inexpensive audio interfaces, and connecting instruments line-in directly, using a Direct Box (DI BOX) in between will substantially improve any clipping or poor performance due to inconsistent Db outputs.