I've been repairing basses and stringing them, since about 1967. Seen a lot of strings... boy, have I ever!
Half rounds, are a total mistake... I could take several paragraphs to explain why- just know there's a number of good reasons, from direct experience, why I say this. A new set of flats, or a broken in set of rounds will sound, feel, and play much better.
The GHS Brite Flats have been available since at least the late 70's. Don't like them so much- too dead in the 'E', and 'A' initially, and after break in.
D'Addario Chromes are relatively recent. They're really GREAT strings. I have them on three of my basses. Bright, like a round new- break in nicely, feel great. NICE even tension across the sets. AND-VERY reasonably priced!
LaBella flats- killer, they've been making them a VERY long time...Joe Osborn used them, and James Jamerson likely did, too... and probably a lot of other well recorded bassists of the 60's and 70's. I used to buy LaBella single flats in 1967. Blue tape back then, red silk ends now, great strings. A little more pricey now, than the Chromes.
Rotosound 'Jazz Bass' flats- available only in super stiff "Steve Harris" gauges until fairly recently. The original heavy set (.95 'A') - 'is incredible, bright, long lasting. VERY high tension. If you're used to light tension strings, you will hate these. The 110-95-70-55 set BENT my Gotoh 201 bridge up like a Rick pot metal bridge. The lighter gauged set is terrific, and easier to play.
Fender flats. Great strings, bright on install, and a bit dull as one would expect, after break-in. 9050 ML is a favorite set of mine. VERY reasonable cost.
DR flats. Beautifully made. Overpriced, and overrated, just like all their strings are, in my opinion. I string a lot of guitars, too- with owner supplied DR's- I still don't get the hype- Ernie Balls are better...and more consistent. and less expensive! Ironic- their bass flats are the best set they make, among all their string sets. But- 60 bucks? Pass.
Ernie Ball flats- good journeyman flat. Not too much to make me recommend them over a superior D'Addario Chrome set. And I LOVE the Ernie Ball Stainless Hybrid Slinky set above all other rounds!
TI flats- the "Holy Grail" of modern flats.
If you have problems with medium or high tension flats, this is a great set. I thought they were well made, and sounded wonderful. I HATED the rubberband -like low tension of them. The deal breaker, plus- they're way too expensive.
The D'addario Chromes- in the 45-100 gauges will please just about any bassist looking to get into flats. They're a LOT like the LaBella flats I used to buy when I was a teenager in 1967. They shouldn't cost you more than 25 bucks after you bribe the salesman at GC with a Gene Simmons autograph.