I'm going to address this in two ways. The first is with the resting rules as presented in the PHB/Starter, and the second is to have a short chat about the alternative resting rules as laid out in the DMG.
First and foremost, we need to talk about how resting works in 5e. Short rests have a timeframe of 1 hour, and long rests have a timeframe of 8 hours. This means that in most scenarios you only want to take short rests in dungeons, and to do so sparingly. To some degree, this is the point of the time frames being this long, dungeons are designed to drain resources from PCs so that final battles in dungeons are meaningful, at least for some value of meaningful.
However, each party is going to have their own comfort level with how many resources are expended at certain points in the dungeon and how much rest their heroes need. How much trouble they have finding a safe spot to rest (or how effective their watches are if they do take a long rest) is up to you as the DM. I can tell you that the first group of players I ran through the starter was feeling mighty uncomfortable by the time they cleared out the second or third encounter, several PCs had nearly died and it seemed like a really good spot in the adventure to take a long rest. How you adjudicate this as a DM is sort of up to you. Long rests are not completely interrupted if a fight breaks out, so it's within your rights to let your PCs rest, but to spring an encounter on them while they are sleeping (though, if you plan to do this, it doesn't hurt to let them know either implicitly or explicitly, that resting here is not safe and may end up triggering an encounter over night). If you really don't want them resting in a certain spot, let them know, they see patrols, or traces of them that seem to pass regularly, or whatever.
That said, in many dungeons, there is no reason that you can't simply let yourself out into the wilderness to go have a nap. This is a possibility in the first cave in the starter set. A 15 minute hike into the woods should reveal a reasonable camp site that won't get discovered by the goblins.
Finally, there are alternative resting rules. They basically allow you to adjust the amount of time short and long rests take in order to defray certain costs. For instance the easiest one changes short rests to 5 minutes and long rests to an hour. This is probably to extreme for your game at this time, but, just the same, it doesn't hurt to modify the time frames to get the game you want to play (these are completely laid out in DMG 267-268).
So, basically, the advise that I'll give you is decide the style of game you want, decide how hurt you want your players to be, and dictate (with some input from them to be sure) how they should be resting based on the style of game you are playing. In the starter (And this is what I've done in my 5e games, including the starter), don't be too hard on your characters for wanting to take a rest, it's not hugely consequential, and they'll probably have more fun if their toys are all available for the rest of the session.
I don't have any knowledge of how long is too long for a message cantrip. However, I do not believe the DM should allow a player to send a message that is too long and truncate it for the recipient.
D&D is not themed or focused around discovering new abilities hidden inside you and learning their strengths and limitations. It's reasonable to assume that a wizard who has fireball written in his or her spellbook knows the range and blast radius of that spell, even if he or she doesn't know the exact damage in terms of polyhedral dice and hit points. Perhaps it's encoding in the arcane glyphs used to write the spell in their spellbook, perhaps the wizard has tested the spell before rushing into battle and scribbled some notes and targeting information in the margin, or perhaps it's just that wizards who cast fireballs on themselves don't tend to last very long.
On top of that, message is a cantrip, which is a spell that the caster knows like the back of his or her hand.
Repeated practice has fixed the spell in the caster's mind and infused the caster with the magic needed to produce the effect over and over. (PHB 201)
I find it highly unlikely that a caster would not know the limitations of their own cantrip, and if a player of mine attempted to do something outside of those limitations (ie, send a longer message), I would stop them. It's similar to how you wouldn't let a player attempt to coerce a black dragon with gold just because the player read the Monster Manual. Their character doesn't necessarily know that black dragons are greedy; that decision doesn't make sense in the context of roleplaying because the character doesn't have the knowledge needed to make that decision. With this, the problem is reversed; the character has more information than the player, and because of that increased knowledge would not make the decision their player wants them to. As a DM, I would notify the player that they're overstepping the bounds of the spell and allow them to rephrase their message or rethink what they want to do. DMs often punish metagaming because players who do metagame to the extent that it impacts everyone else's fun often have other issues that make them less fun to play with. However, with..."eso-gaming"? ("meta" means outside in Greek; esoteric means inside. I'm thinking too hard about this.) With "esogaming", a player could be sleepy, read through their character sheet too fast, didn't realize you've come up with an alternative house rule for this situation, or had a different interpretation of a vaugly-worded spell or ability (as is the case here). Correct them gently and I doubt they will make the same mistake again.
Best Answer
Long-distance: Sending
3rd-level spell: "you send a short message... to any creature with which you are familiar.... You can send the message across any distance...." (PHB p.274)
You could purchase use of the spell from a mage-for-hire; Adventurers League guidelines* would suggest you're probably looking at 90gp per usage.
You could hire someone with the ability to cast the spell: What's a good pay rate... might have some useful advice on that matter.
You could invest in scrolls or potions of sending. (In any world that makes a modicum of sense you've got to have 5th-level wizard drop-outs churning this exact item out as a way of making a living.) The DMG has advice on fashioning magic items that may help you and your GM.
You could train up the talent yourself—befriend an NPC, bring them along to fifth or sixth level, then station them at HQ.
Sending Stones are a similar magical item
You could invest in sending stones (DMG p.199) which allow for the casting of sending once per day; the DMG would price them at 101-500 gp (uncommon item), though the Sane Magic Item Prices index would put them at 2000 gp. (With thanks to @anaximander for the pointer.)
The spell's there; the possibilities are endless.
Intra-city: Animal Messenger, or human messenger
2nd-level spell: similarly short message, range of 50 miles, a tiny beast delivers your message in your voice. There's the possibility of your messenger getting nabbed along the way, but at half the price* you can send redundant messages and still save 10gp!
Of course, at this distance and cost it's not clear why you wouldn't use the solution known since time immemorial: street urchins. (Available at 2cp per mile, per PHB p.159 "Services", thanks to @Sebkha.)
* - a list of spells available through "Spellcasting Services" is provided in the front-matter of every Expeditions module. Remove curse and speak with dead are the only two third-level spells listed, at a price of 90gp each. Various second-level spells are priced at 40gp each, divination (4th-level) is listed at 210 gp.