some advantages

you can hear a representation of your work using score playback (not the same as acoustic realization, but better than nothing)
the ability to edit, re-edit, change layout and spacing, font style and so on
make good looking and readable scores and parts, independent of your 'hand writing'
easily extract and print parts

some challenges
some versions of the software can be expensive (some are free, see info below)
there is a learning curve, but it is manageable if you start with easy notation projects
some contemporary / experimental notation ideas can be difficult to express, or might require additional tools

basic notation process (similar steps common to most notation software)
music technologist Dan Hosken brakes down the process into three parts (from his book, introduction to music technology):
supporting links from the chapter are here
setup - this is when you define the basic parameters of the piece, such as number of staves,instrumentation, clefs, key and time signatures and so on. sometimes this process can be made easier by using 'setup templates'
entry - the entry of notes, dynamics, phrasing, articulations, and even lyrics or chord symbols, if needed. This is also a good time to proof and edit your work, and using audio playback can help this process
layout and print setup - once the musical data has been entered, the layout can be customized to best fit the materials. Page size, measures per system, systems per page and so on, can all be adjusted to make a professional and readable score and parts

software options

Free:
MuseScore - probably the best, most versatile free option that is WYSIWYG i.e.; graphic entry / interface (runs on mac, windows, linux)
Finale NotePad - scaled down (currently free) versions of Finale - lots of limitations, but good for getting started (windows only)
Noteflight - free online application; access to more features requires Noteflight Premium and a yearly subscription - comparison is here)
LilyPond - text -based input, very different from the other programs mentioned - (runs on mac, windows, linux)

Cheap-ish:
Finale PrintMusic - all three Finale products are listed here (windows only) - probably not worth it, since there is a discount on the full FInale program
Sibelius First - light version of Sibelius (comparision of Sibelius options is here)
Notion - another competitor in the 150.00 and under category

Full Featured (and more expensive - some have aneducational discount, or monthly subscription option)
Finale
Sibelius
Dorico

scanning

scan into finale using the included SmartScore lite - general scanning instructions are here or you can watch the scanning video here
more info about SmartScore versions and upgrades options is located here
scan into Sibelius using the included PhotoScore lite - scanning instructions are in this document (see section 2.2)
a comparison with PhotoScore pro is here

Where to go from here?

option 1 - free / easy - go to the Pratt 103 computer lab (during walk in hours) if you want to use the full version of Sibelius or MuseScore

To work on your own computer (for free):
option 1 - download MuseScore and get started! Check out the 'getting started' video tutorials on the front page
option 2 - log in to Noteflight and get started
option 3 - download Finale NotePad (if you are using Windows OS) and get started
option 4 - download Sibelius fee trial here and get going
option 5 - download Finale 30 day trial here and check out the learning resources here


*take it slow / be patient... maybe work with a friend and learn together? try to do a simple project first, maybe something useful drawing from your theory / musicianship classes, or your private lessons? talk to / ask your teachers and friends for advice or help
(some may be quite good at this, other may not) - lots of good web resources + books
lots of resources on linked in learning dot com

Other interesting resources (scores, MIDI and XML files)

Project Gutenberg: Sheet Music examples
International Music Score Library Project (IMSLP)/Petrucci Music Library
Listing of public domaine music file sites
Meta site listing other MusicXML sites