yes, there are benefits to using a subwoofer. almost all pc speaker systems use satellite sized speakers (small) which lack the ability to recreate low end bass. a subwoofer fills in this gap by providing low end extension.
you have 4 options on that budget:
-2.0 pc speakers. perhaps the nicest sounding ones are the t20/t40 from creative however they lack bass. good for people with limited space and who arent bothered by a lack of bass whether to keep vibrations from travelling through walls in shared housing or preference.
-2.1 pc speakers. similar to 2.0 but with a small subwoofer for bass extension. the logitech sets like the z323 or z523 are sufficient and decent quality for budget though tend towards more boomy bass sounds. the creative creature iii and soundsticks (though the sticks are above budget) are a bit more refined.
-2.0 powered hifi speakers. i cannot recall any sub $100 units off the top of my head but you may certainly be able to find some self powered bookshelves for $100 or lower either new or used if you look. the nice feature about self powered speakers is that you do not require an amplifier although the negatives are that you are highly limited by models.
-2.0 unpowered speakers with an amp. this gives you a bit more choice over self powered units as more models are available to choose from. a good start would be this list http
/www.audiorumble.com/best-bookshelf-speakers/under-100/ paired up with a cheap amplifier. the lepai 2020a+ is often used on some of the easier to drive and cheaper models although it is well worth investing in a much better amplifier.
generally hifi and home theater equipment is going to sound quite a bit better than pc speakers although generally has higher cost investment as well. its entirely possible to build a hifi set for under $100 using some budget bookshelf speakers and budget amplifier however and is worth looking at. bookshelf speakers are able to extend deeper into low end bass so as long as deep bass is not required they can, depending on models and amplifiers power to handle the speakers, handle bass response fairly well.
pc speakers are commonly available and everything is contained in one box which makes them the easier option, at the expense of being only adequate. although it is true some of the nicer sounding ones arent half bad at all - just not up to the level of hifi/theater speakers.
if you had more of a budget, there are of course other options including using better quality theater speakers (this is the route i use myself... i have a full set of klipsch speakers).
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