in my working voltages with base resistors higher than 2K none of the transistors go into saturation mode that I need.
I don't know what transistors you're using, but I don't believe for a second that they are not saturated at the couple mA of current you're flowing through them. After all, that's what you show in the question, even though I have an inkling that's not the case. See why providing too little information wastes your and our time?
The transistors would be considered saturated at V(CE) of about 0.1-0.2V, and I can guarantee that that's the case in your circuit as long as it's what you're showing.
So you're either misunderstanding what saturation is, or have some truly atrocious transistors, or are making a measurement mistake, or you're not telling us something - possibly some combination of those.
Higher collector current will be drawn by removing the LEDs, and even then lousiest of transistors I got in my junk box get saturated in this application.
I assume it's 3.3V logic and VCC. Suppose the transistor beta is 40. None of the modern transistors you buy would be that bad at the currents in your circuit.
They still saturate just fine with LEDs removed and 10k base resistors. With LEDs added, the saturation voltage is even lower, since only 30-50% of the current flows compared to when the LEDs were shorted out.

simulate this circuit – Schematic created using CircuitLab
You can simulate this circuit, click on SW1 to select it, then use space to flip back and forth between logic states on the input. The circuit works as you want it to.
With more reasonable transistor gains, it performs even better, letting you use larger base resistors.

simulate this circuit
Adding LEDs back into the circuit decreases the currents and lowers the saturation voltage even further. It's inconsequential either way.

simulate this circuit
The schematic was the simplest way to explain that I want a single input control two transistors of different type.
Absolutely not. Your circuit implies a lot about the load current and load behavior. A schematic is a graphical language to convey information. When having a specific schematic and no text to indicate otherwise, the schematic is all we got to work with to answer your question - it speaks in the words you didn't.
From your scattered comments I gather that you're driving a much heavier load than you're not telling us about. For that load, you will need either logic level mosfets, or two stages of transistors.
See, it is really important to actually say what you need, not to imply things with very little experience. You have asked a question and you will get answers exactly to that question you wrote, not to whatever you know but don't tell us. We cannot read your mind.
Had you asked about your real application, you'd have gotten relevant replies immediately, without having to go back-and-forth with comments and dosing the information in little drips.
I want a single input control two transistors of different type
Are sure that's what you need, or is that just a particular solution you have in mind, but not the actual need? If so, that woul be a case of an XY Problem.
Given the sparsity of information, you may as well just want one logic output to control two loads: one load active when the level is low, another load active when the level is high, and one chosen load active when the output floats - or perhaps no loads, essentially tri-level logic. It may come as a surprise, but that can be all done with transistors of just one type - so transistors of different types seem to be a spurious requirement that doesn't really capture what you need, just what you think the solution should be.
Now, if you knew what the solution is, you wouldn't be asking the question. Since you asked, you have to presume you don't know the solution, so don't presume one - but do tell us what you tried, after the problem was clearly stated in absentia of a particular solution that may turn out, after all, to be non-ideal, or just a kludge, or whatnot.
From what you're saying, let's see what current your actual loads need: you claim the transistors stay saturated with 1k base resistors, but nothing higher. Let's also say your criterion for saturation is \$V_{CE} \le \frac{1}{2}V_{BE}\$ - so, less than about 0.3V.

simulate this circuit
We can now run a parameter sweep for the value of the load resistance RL, looking at the collector current and voltage:

Saturation occurs with approximately \$R_L\ge18\,\Omega\$, and you seem to need about 250mA of load current. To get some factor of safety, we can assume 0.5A load current, and design for about 1A load current.
We note here that 200mA is the maximum collector current for the ubiquitous 2N3906/2N3904. So we need higher-rated transistors as the output stages, and a driver stage preceding them.
Now, it could be that you're using a medium-power transistor, with a lower gain, but higher collector current capacity. This doesn't change much, since it would need even more base current to get saturated for a given load, so the assumption of the load current is conservative and should cover your presumed needs.
So, we could have the following circuit:

simulate this circuit
It will easily switch a couple amps, with saturation voltage below 0.1V. The total dissipation in the circuit is below 0.5W.
The load on the GPIO pin is < ±0.1mA.
With the GPIO pin working a bit harder, we can get rid of one stage, and get rid of the separate pull-down resistor:

simulate this circuit
The GPIO current is 2mA in the high state, and nil in the low state.
Now, those circuits don't switch fast - it'll take several microseconds due to base charge due to saturation. If you need faster switching, additional desaturating transistors would be needed.
And, of course, we don't need two kinds of transistors. And we can get rid of one resistor as well :)

simulate this circuit
The GPIO current in the high state is 0.3mA, and nil in the low state.
Since all transistors saturate in this circuit, the switching is not very fast. We can do something about that. First, let's desaturate the 1st stage transistors by reconfiguring them as emitter followers:

simulate this circuit
Now we can add desaturating transistors that will bring the 2nd stage out of saturation on turn-off:

simulate this circuit
NOT1 and VCVS1 model a 3.3V inverter, such as 74LVC1G04.
This circuit switches in less than 1μs. Turn-on can be sped up by adding a small speed-up capacitor - like 20pF - in parallel with each of R1 and R2.
The GPIO load is 0.2mA during logic high state, and nil during logic low state.
If the load isn't particularly capacitive, the inverter becomes unnecessary:

simulate this circuit