Yes, there certainly are a lot of choices. Factors to consider: disease resistance? Are you ok with spraying for diseases? You mentioned polyanthas, which are quite informal and old-fashioned. I like such roses for color from a distance, but for up-close admiring, I'm partial to roses with more developed form. I have just around 3 dozen roses, all in large pots. For a balcony rose, I'd go with a mini or mini-flora. We don't live in very different regions, so hopefully the roses that do well here in Louisiana will do well for you too.
One rose that has done great for me with minimal fuss has been the mini Absolutely. Pretty form, interesting and varied blend of white, apricot, yellow, and pink. Mine was purchased very small, took a couple years to really come into its own but then has looked terrific, bushy, usually in bloom with rapid cycles and lots of blooms. Nearly disease-free for me with minimal spraying. It has even done well with only a couple hours of direct morning sun and a couple hours of sun before sunset, because I have it on the northern front corner of my house. Visitors often make admiring comments.
Some others that have been good bloomers for me, and bushy:
Electric Lady: intense deep pink with an apricot-blush center. This is a very compact miniflora, very prolific and great form. But must be dilligently sprayed to keep blackspot at bay.
Always a Lady: beautiful and very porlific clear lavender mini (no hint of pink) with impressive sweet fragrance. Blooms in distinct cycles.
Caliente: I could "almost" consider this the perfect red mini. It has a little fragrance, blooms continuously and a lot, the buds and open blooms are as exquisitely formed as any minis, and the color is intense, rich red. I'd say it has average blackspot resistance. The biggest criticism is that the blooms do not age well, bluing in an unattractive way. But it blooms so much that if you're willing to pinch off the aging blooms regularly, you'll still have a gorgeous prolific bloomer. Looks great as a specimen in a pot.
Hot Tamale has been a great old standby mini for me. Terrific flaming yellow/pink/orange combo. Great bloom form and prolific, though in distinct bloom cycles. The bush stays compact and bushy. Supposedly fragrant, I rarely detect any fragrance from this one, but so what.
Good luck with your quest for the ideal mini. It can be fun searching!
Mike

Love the suggestions for the minis. I want to visit Kimbrew Walter roses soon and get quite a few minis for some small beds and will look for those.

What I am actually looking for is a bigger rose that can be seen from downstairs, looking up to the balcony that is shrubby, keeps its leaves well and blooms lots. I could get one of the Knockouts....and I do like them and grow them, but was looking for something different.....Thought about Cecile Brunner, have never grown it, but the color is paler than I would like [even tho I said color doesnt matter!] I plan to get a few Sweet Chariot roses in another smaller pot as they bloom alot and trail - but wanted a bigger shrub for the main pot. Thanks....

'Marie Pavie'?

Here is a link that might be useful: MP @ helpmefind

This rose does so well for me in a container that I always recommend it. It is hard to find a large flowered rose that stays compact for years and years in a warm climate area, but Lady Mitchell does this in spades. Aside from almost continual bloom, it has nice shiny leaves with better then average disease resistance. The photo below is not a particularly good one, but at least it shows its nice rounded habit and bloom sequence. Available from Heirloom roses. {{gwi:224880}}

This is an upclose shot of its blooms:
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I second the vote for Marie Pavie. She has been heat tolerant, disease resistant, ever blooming and fragrant for me- even growing in alkaline clay. Ducher and Francis Dubreuil/Barcelona have grown very well for me in a container.