Starting my players in prison

I am very much new to DND and I started right off the bat dungeon mastering, for our first session we had lots of fun and I’m working on putting together another one shot and using a premade campaign, while researching for the premade campaign I started thinking of when I’m going to do my own home brewed campaign. Now I won’t do this big home brew game until I have a bit of experience with my party, but I’m thinking of maybe starting it with my players all in prison, I feel like it’s a fun creative idea and challenge for them near the start of a campaign. But I’m second guessing myself and maybe…just maybe thinking it’s a bad idea. Anyone have any tips if I were to start a campaign with this? Or maybe tell me if this idea is bad or not. 

There is nothing wrong with starting in prison.  But how does starting in prison makes sense?

Does this mean all of the PCs know each other?   Are they in a nearby cell block so they can talk and get to know each other? 

How do you explain a LG alignment Paladin being in Jail?

Will they all be released because they serve their sentence or do they have to break out of jail?  

What gear do they have as all of their possessions would have been confiscated on the way to jail?

Grab yourself a copy of Out of the Abyss. The adventure begins in a prison and the first section is the prison break and subsequent flight from the captors. It'll provide a great insight into what you think works or does not work. With that knowledge it'll be easier to develop your own setting. I'd also suggest looking up Prisoner 13 as that might too be of help to reference and steal ideas from for your own setting. 

I'd advise remembering that False Imprisonment can be a thing, as well as the fact that some nations or territories might outlaw things that other nations might not. This gives a great avenue to allow a convincing backstory that the Lawful Good player character has ended up in prison because they tried to haggle with a merchant. That innocuous act might be perfectly acceptable in their home nation, but in the one they are currently imprisoned by carries a sentence of six months or something. Having this kind of vibe allows you to maintain some flexibility for player character options. 

Looking at Out of the Abyss while the prison there is not just a prison but an outpost involved in the trafficking of humanoid labour, it does provide some solid lessons. The PCs are under immediate threat. The drow guards don't brook any revolt or scuffles. They'll fire crossbow bolts tipped with a poison that will knock out the characters. If there's signs of a rebellion, they'll simply pick a random prisoner and throw them to a nearby giant spider as a warning to the others. In short the threat to the lives of the PCs is high from the very beginning. To escape their fate, they need to escape. Now, of course you don't necessarily need to touch on the same dark themes that OoA touches on. You can simply have this imprisonment be fundamentally unfair. Life imprisonment may be the norm for the nation in which the characters find themselves. Maybe other prisoners are simply much more threatening and escape is the only obvious way of avoiding regular beating by fellow inmates. Whatever you decide it's for this reason I recommend at least flicking through the adventures I've mentioned.

Ultimately, if you're a new DM though and new to D&D at large you don't know yet what is creative or challenging. Get yourself to a local library and look at the official adventures. Read through them from a design point of view. The reason you'll so often hear new DMs be told they should start with a starter adventure like Lost Mine of Phandelver is because it introduces the basics of the game and the expected ebb and flow of a campaign very well. Similarly something like Curse of Strahd shows you ways in which to tweak and modify those rules once the players have picked up a bit of experience playing the game. You don't necessarily need to run every adventure, but just like any aspiring writer should read widely; every DM should read adventures. It'll better help you decide what does and does not work in your mind. 

Starting in prison can work just fine, just keep in mind that the start of a campaign sets the tone. A campaign that starts in prison and with a prison break indicates it will be a campaign where the party is on the wrong side of the law, potentially running from the authorities and likely instigating some sort of rebellion against the current corrupt authorities. If that's the kind of campaign you want to run go for it! and tell the players ahead of time to come up with reasons for why they are in prison. But if you want to run a classic heroic campaign where the party work for the king and become his trusted knights / advisors probably not so great to start it off in a prison. 

There are so many options for a campaign starting in a prison.

1)No Memory - The prison could be a large city prison where the characters wake up with no memory of why they are in there. They assume they are wrongly imprisoned for murdering the beloved prince/ss and sentenced to be executed. They escape but find themselves not only hunted down by the town guard but also another mysterious group. The group spend the game trying to prove their innocence and discover what happened but as they backtrack and learn the truth, they find they did actually murder the Prince/ss.... but for good reason.

2) Exotic Location - The prison could be in an exotic location - beneath the sea in a Saughins Sunken City, a necroplis where they are soon to be part of a undead feast, on a leaking ship forced into service by pirates, in the slave pens ready to be auctioned off (perhaps into a gladiator school?), beneath a Duegar City etc. All of these can set the tone foe a whole campaign or as a glimpse into later events in the campaign. If the location is not something you want to explore in depth, the characters can magically gate/teleport to a more mundane locations after the exciting first chapter.

3) Turn the tables - perhaps the characters are not ALL prisoners. Maybe half are and the rest a prison guards or visitors that help with the escape when they witness injustice or terrible brutality and see an opportunity. Perhaps a riot occurs and a mass breakout where they all become escapees. Some of the prisoners that escaped, earlier had run ins with the group and later seek vengeance. Some of the escapees could be particularly dangerous or about to unleash a horrendous crime that the party now feel responsible for and try to stop. 

4) Wayward youths - the party may have been part of a community (Dwarf Clan, Elven Twilight Town, Cloud Castle) and been placed into the prison as a wake up call for all the misdemeanors to try and turn them around. They meet a strange prisoner inside and help them escape showing them secret tunnels into and out of the city/community. Their new friend uses the secret doors to break into the city with an army/strike team and kill the leader. Perhaps it is even more dramatic as the villain returns with an army and completely destroys the town and kills the characters families. The groups goes into hiding but later returns to try and bring their people back together and reclaim the community from the very villain they helped all those years ago. 

5) Spies - The group are in prison as spies to befriend and get information from. No one has been able to get close to one of the Prisons most notorious criminals and time is running out (death bed, execution, war approaching, magical gate closing etc). The alternative is that the group don't know the prisoner they have befriended at the beginning of the campaign is anyone important and the story/map/trinket they shared is anything of value.