PjD1st is kind of a doozy because while as far as pure skill is concerned, it's the easiest to fully complete (due to its more simplistic mechanics compared to later games in the series), it's also one of the grindiest roads to completion possible. Once you've perfected all songs and unlocked all modules, the rest (room items and picture gallery) is entirely up to RNG, for better or worse.
There are a total of 36 songs in Freeplay Mode, which is the only thing we're concerned with (there are additional songs in the Miku Room and the DLC Packs, but they do not count for completion). By default, only EASY and NORMAL difficulties are available, and clearing a song on NORMAL unlocks HARD and the ability to view its music video outside of gameplay. It's recommended to play on NORMAL, as EASY does not unlock modules or HARD mode. Each song is further divided in difficulty based on how many stars it has, from a range of 1-5 (with two exceptions breaking the scale on HARD, maxing out at 7).
Songs are sorted into one of six colors, and each color is its own unlock chain. Pink songs are by ryo and have a theme of "love". Blue songs are by kz and have a "sci-fi/future" theme. Orange songs are by OSTER Project and have themes of art/creativity and "colorful feelings". Yellow songs have a nature theme. Sky Blue songs have themes of school and the four seasons. White songs are all popular songs on NND at the time, usually about Miku herself. Pretty much every song that wasn't commissioned was released around Fall 2007 - Summer 2008.
Six songs are unlocked by default: The World is Mine, Far Away, Ame Nochi Sweet*Drops, Kouya to Mori to Mahou no Uta, The secret garden, and Koisuru VOC@LOID.
Unlocking all songs is pretty straightforward, but if you'd like a more detailed guide, click here.
Most modules have two conditions that must both be met to unlock them. The first is by clearing a song on a specific difficulty and gaining a minimum rank. The second is by clearing that same song regardless of difficulty while reaching another condition (such as a particular combo, score, or even simply number of clears). In some cases, you have to clear a song while using a specific module.
Since the unlock condition of all modules involves clearing songs, the following paragraph will be my recommended order (assuming a moderate to high skill level). If you'd simply like a basic unlock guide, click here.
The first thing you'll want to do is clear every song 5 times on NORMAL, using Hatsune Miku Original. This should unlock every song and most modules, including Hatsune Miku Swimwear. Next, go through each vocaloid (Rin/Len/Luka/MEIKO/KAITO) and clear every Miku song on HARD either 1 or 5 times, depending on how consistently you can get a GREAT rank. Once you've unlocked your character's swimwear, switch to the next vocaloid. While you're at it, clear the Rin/Len vocal tracks once too. After the lengthy grind, you should have every module except Space Channel 5 and Hatsune Miku Swimwear S, which require you to clear specific songs using specific modules unrelated to the general swimwear grind. Do those real quick, and you're done.
The Miku Room is pretty rudimentary compared to the DIVA Room of later games. It's also the one thing keeping you from true 100% Completion. For you see, every item unlocked is determined by RNG. The Project DIVA MASTER BOOK has more detailed drop rates than what's shown in-game, so click here for deets on that. The most important thing is this: you can unlock room items at any difficulty, so honestly just pick a song and grind. Miku-Miku ni Shite Ageru♪ (Shiteyan'yo) is best for this due to being the shortest song in the game.
There are 197 pictures in the Picture Gallery. The first 59 of those are random loading screens, so you'll see them all eventually. The last 17 are related to unlockable posters for the Miku Room: again, it's up to RNG and you'll likely have to grind a lot for them. The remaining 121 are unlocked by clearing the five songs in the White Tag that lack 3DMVs (they are slideshows instead).