“There is no point in doing this [from a game mechanic perspective].” The sorcerer is just the stronger class, and even the feature-heavy first level of bard does not compare to simply having better spells sooner (see 1. Spellcasters should not multiclass in this answer for more details). Thus, the best mix of nine levels for bard or sorcerer is Sorcerer 9. That said...
Sublime Chord
The best way to multiclass bard and “sorcerer” is to not have any sorcerer levels at all, but rather take the sublime chord prestige class from Complete Arcane. This class requires Bardic Mustic and 3rd-level spells, but rather than progress bard spellcasting, it has its own spellcasting with 3rd- to 9th-level spells from the bard and sorcerer/wizard lists. This spellcasting is Charisma-based and spontaneous. It also progresses bardic music, and gives several special “magic themed” songs.
So a Bard 10/Sublime Chord 10 casts as a 10th-level bard and also has separate spellcasting with spells of up to 9th-level that come from the sorcerer/wizard spell list (or bard list). It has the ability with music of a 20th-level bard, except some of the songs are changed to be more “magic themed.”
Since spellcasting is the only sorcerer class feature aside from the familiar, having spontaneous Charisma-based spellcasting off of the sorcerer/wizard list, and then taking the Obtain Familiar feat, makes you effectively identical to a sorcerer. But this progression is much smoother, you end up with level-appropriate power at higher levels, and sublime chord is really cool. The only problem here is that, before 11th level when you take your first level of sublime chord, you have no mechanical representation of being a sorcerer. But bard and sorcerer spellcasting are fairly similar, and you can take Obtain Familiar at Bard 1, so it should be easy to continue to call yourself a sorcerer at lower levels.
Spellswording
Worth mentioning: Champions of Valor has a variant paladin, the harmonizing knight, that gets Inspire Courage +1, 1/day instead of at-will detect evil at 1st level. In the Forgotten Realms, this requires you to worship Milil, a goddess of music; in other settings, it would have to be adapted to some appropriate patron. Anyway, all paladins get the excellent Divine Grace at 2nd level, adding Charisma bonus to all saving throws. As such, Paladin 2/Bard 8/Sublime Chord 10 becomes an excellent variant on the above build: you trade 1 daily use of Inspire Courage for full martial weapon proficiency, a bit more HP, +1 BAB, and adding your Charisma bonus to all saving throws. Since your Charisma should be high, that is a very nice bonus. Adding paladin is not an option for all characters, of course, but if it is, do consider it.
For spellswording as a bard, whether you dip paladin or not, I strongly recommend the Snowflake Wardance feat from Frostburn, if you have that book. Other excellent options include the harmonizing weapon property and crystal echoblade weapon from Magic Item Compendium.
Finally, if you have Tome of Battle, taking a level of crusader for the Song of the White Raven feat is an awesome option, dramatically amping up your physical prowess while allowing you to start performing Inspire Courage as a swift action. It also opens up the interesting possibility of using the jade phoenix mage prestige class to advance sublime chord spellcasting, which would be ideal. Note that Paladin 2/Bard 7/Crusader 1 still just qualifies for sublime chord, too, if you want to do both. I recommend taking the crusader level at precisely 9th level, so you can simultaneously take Song of the White Raven, and have Initiator Level 5 so 3rd-level maneuvers and stances are available to you.
Race
Generally speaking, race isn’t all that important; human is probably your best bet just because bonus feats are awesome. But anything without a penalty to Charisma or Constitution is probably fine (bonuses to Charisma are really rare and always paired with a penalty to Constitution, so there is little to be gained there). Even penalties to Charisma or Constitution are bearable, but why would you?
However, in the case of anyone with bardic music, the benefits of being a dragonblooded race have to be mentioned. And since there’s a dragonblooded human race, silverbrow humans from Dragon Magic are almost-certainly your best option. They trade the humans’ bonus skill point for the Dragonblood subtype, which among other things qualifies you for the excellent Dragonfire Inspiration feat from the same book. Highly recommended.
See Also
Best Answer
The 5e Bard is a more powerful character than the 3.5e Bard, but not nearly as good at buffing his allies.
To start with, the 5e Bard gets full spellcasting all the way up to 9th level spells, where the 3.5e Bard got 2/3 spellcasting, topping out at 6th level spells. This is, in some ways, the biggest change, and it has a huge impact on the Bard's power and flexibility. Their spell list doesn't have the raw power or versatility of the Wizard, but it's pretty solid. And, of course, they get to add stuff to it. More on that later.
The next thing they get depends on your choice of College. Valour Bards get Extra Attack, and a bunch of proficiencies, that put their fighting ability roughly on par with that of a Ranger. Lore Bards, on the other hand, get bonuses to skills that make them arguably the best skillmonkeys around. This honestly isn't a huge change; the 3.5e Bard was already a pretty reasonable fighter and a great skillmonkey.
What's really different is the Bard's specialty, inspiring allies. This has, in all honesty, gotten substantially weaker. Instead of continual effects that boost all nearby allies, the Bard now has the ability to give a single ally a one-off boost. It's slightly more flexible in that the ally can choose which roll to add it to, and the Colleges add even more uses, but it still amounts to far less of a boost. What's even worse is that, for the most part, the Bard can no longer affect themselves with their inspirations.
Spells can help alleviate this, but buffing spells have also gone under the hammer. For the most part, because of concentration, you can only have a single buff spell active at a time. And, just like your inspiration, most of the good buff spells have been changed to only affect a single target.
What these changes amount to is a character who no longer sits at the back buffing, not just because they have other options, but also because they can't. The dedicated buffer is no longer a valid playstyle. You can give an ally inspiration every turn, but that still leaves your actions free. You can use your first turn to cast a buff, but you won't be able to do that on later turns.
Luckily, there's some good news coming. The 5e Bard has a unique and extremely powerful feature that I haven't talked about yet. Magical Secrets allows a Bard to select a few key spells from any spell list. This ability is incredibly important, because those spells (especially the first 2 you get) can shape your character's playstyle. The most infamous example is Swift Quiver. This is a 5th-level Ranger spell, which means it's normally only accessible at level 17. However, a Bard can learn it at level 10. This allows a Valour Bard to make 4 attacks per round with a bow at level 10, long before a Fighter or a Ranger.
So, what's the takeaway? (Or, if you're that way inclined, tl;dr)
The 5e Bard is a versatile and powerful character who can excel at most things they set their hand to. With a bit of work, so was the 3.5e Bard, but relative to other classes, I think it's fair to say the Bard is more powerful in 5e than it was in 3.5e. On the other hand, the 3.5e Bard is much better at buffing his allies than the 5e Bard.