I did this sort of circuit many years ago (1980s) as I designed LED panels having anywhere from 20 to 2500 LEDs.
It seems that it isn't common knowledge these days that a blinking LED is preferred to a steady lit LED. It not only consumes half or less power (lower heat and resistor concerns), but it actually appears brighter to the eye. So the idea of trying to smooth the 150-160v peak from a bridge rectification is not so valuable. Light flicker at 120Hz (full wave rectification) is undetectable to the mind, but causes more effect on the optic cells of the eye. About 100Hz is ideal.
Another consideration, as you decide how many LEDs to parallel rather than series, is the maintenance and cross weakening effects. A single LED becoming weak can disrupt the entire matrix. I recommend, and always used, lower voltages either by saturated transformers or switching SCRs/Triacs, to power an array of shorter series. If you try to string all of them in series, or as many as possible, you start having dimming concerns that force you to one-by-one isolate which LED is causing the variations (the Christmas tree lights effect).
Also, by using a saturation transformer, you further restrain the power source variations that can easily cause substantial dimming as the power company switches loads and circuits. In most cases, a small voltage regulator is advised, perhaps an array of zeners, so as to give room for source variations without affecting performance.
25ma sounds like a lot to me. I never had a case needing any more than 13ma, but maybe you are using some newer high power devices. You do NOT want to run them at their max rating. An LED will last forever if you ensure that it never exceeds its max. If you allow for only a second for it to get to max current, it will slightly melt and become comparatively dim if not burn out entirely.
Power efficiency should be considered. It is not merely a waste, but an issue of heat production which shortens the life of all components. Arranging the best array matrix reduces the need to use resistive components. Any voltage stepdown will produce heat waste. Switching circuits are easily purchased and are the most power efficient means to reduce voltage. But cheap saturation transformers do the trick although might wear out sooner.
There are many ways to do what you are talking about. I wouldn't worry about trying to produce a steady DC.
Also, realize that typically, LEDs do NOT come matched. Each, although within specs, is still different than the others. Thus don't go assume that every LED will yield the same effects. It won't. If you string 12 together and another 12 together with the exact same voltage applied, you might get substantially different illumination. If you want something that actually appears professional, you need to carefully choose which LEDs you string with which other LEDs. Its a pain, but if you do not current regulate, it is often required.
Current regulation is best handled by purchased IC modules designed, usually with junction diodes, to ensure that you get the proper current regardless of device variations and source variations (within limits of course). LEDs produce illumination proportional to current, not voltage.
In addition, consider what is going to happen when even one LED burns out. Normally an LED will melt into a short circuit before it opens up. If your series string is designed too close to the max rating and the string is short, you will most probably burn and damage the entire series just before it blinks out, having to replace all of the LEDS instead of just the one that first failed. You the "Typical" ratings in your designing, not the max. According to your data sheet, that would be 20ma, not 25ma. But if, for example, you only had 2 LEDs in each string, the second LED that had not failed will suddenly and for a short time, have twice the voltage on it and will melt. Heat is the issue even though you can have as much as 100ma for a very short pulse.
If you design the string using a 20ma expected current and you have 10 LEDs per string, if one shorts out, you will end up with 3.5 volts per LAD in your string. As per your data sheet, that would produce about 50ma through each other LED. That would burn them in pretty short order.
To ensure that you have less than max current even if one shorted out, you need 20 or more in each string. 20 would leave you at 3.38v per LED and about 25ma if one shorted.
You might also want to note that you can buy such strings ready made these days. They make Christmas tree strings with LEDS. You can find them online I'm sure and your cost might be less than trying to build one yourself unless you happen to already have the components.