Starting dip at first level, let's see:
1. A fighter is the most obvious. You get heavy armor and a fighting style, along with all the weapon proficiencies. This can be helpful for most every build. Certainly classes that could use the armor proficiency, but if not for that, then for the fighting style.
2. Starting as a cleric can be useful, especially to another spellcasting class. They can get up to heavy armor proficiency along with shields, and it won't hurt their spell slot level progression. This is mostly beneficial to the wizard who can scribe scrolls at higher levels based on slots.
--the knowledge cleric can be good for characters who want to focus on skill proficiencies.
3. A starting sorcerer dip can be great for a warlock who intends to wear the potent robes. If the draconic subclass is chosen then the warlock will ultimately have a decent AC wearing the potent robes. This is great because of the benefit those robes offer to the eldritch blast. It also happens to come with the much coveted constitution saving throw proficiency.
4. Beginning with a monk dip can be nice. It gives you the ability to use your dex with any weapon you're proficient with. For example, if Shadowheart started with a high dex and a level of monk instead of cleric, she'd be great with the spear without having to invest any points in strength. That way she could be sneaky, wise with cleric spells, and effective in martial combat. All of which a dark justiciar is supposed to be.
5. The wizard has to be mentioned. A wizard can scribe spells from scrolls based on castable spell slots as opposed to wizard levels. So if you have a first level wizard and an eleventh level cleric, the character can still scribe sixth level wizard scrolls and cast them. Not many per day, of course, but enough that it can arguably be worthwhile, especially when you consider the inclusion of spells like curriculum of strategy: artistry of war.
