Ground and power planes make it a whole lot easier.  Plan on a few board spins if you try to do without one.  

In a previous life I designed single layer PCB receivers for commercial (aka cheap) applications below 200 MHz.  What I found useful was to never use a ground symbol in my schematic in the RF and IF sections.  If something needed to attach to ground I drew it wired to the ground net.  This helped to show in the schematic where the 'ground' current was flowing.  If it got too messy and too loopy I knew my single sided design was getting into trouble.  

With two receivers you'll need to be very careful about crosstalk and interference between the two circuits.  

The AM commercial band hardly requires a low noise amplifer. Because of atmospheric noise levels the SNR is set by the environment, not by the amplifer. What is often required with short whips is an amplifier stage with extremely high input Z (often called 'active antennas').

There are plenty of AM & FM antenna preamplifers (I'm not going to call them LNAs) found in automobile antennas; like the Fuba-type rubber whips often seen on the trailing edge of VWs. I believe that most of these are simply broadband amplifiers that probably have an input network to match the short whip to the cable. The one VW whip that I tested worked very well on the shortwave bands as well as AM & FM. This indicates that the design simply covers the entire AM to FM commercial bands in one continuous swoop. This approach has much to recommend it.

What is your application? What sort of antenna? What sort of radio? Is it an 'automotive' application?

Hi again,

yep, the application is an automotive one. The idea is to design the AM high impedance amplifier and the FM amplifier using both sides of the pcb in order to reduce its size. I´m using 50R antennas and the load is 50R for FM and 300R for AM. Do I need to use internal ground planes? Do I need to take into account anything when doing the layout? Will it work without any ground plane?

There exists a 50-ohm antenna covering the entire 3:1 frequency range of the AM broadcast band? That will fit on a car? Anyway...

You shouldn't need much gain on either band - most car antennas are totally passive and work fine.

Dynamic range and strong signal-environment performance is probably much more critical (driving close to in-band transmitter sites).

Matching in and out Z is going to be a head scratcher (I doubt anything is as simple as nice 50R or 300R).

Make sure you roll off the gain and keep it low up to the maximum frequency of your active device(s). If you use devices with gain up to microwave frequencies, then you need to pay attention to gain and feedback up to those frequencies (to prevent oscillation).

Also, don't forget to account for an added GSM mobile antenna installed a few inches from your antenna. You should probably include some components to filter out such frequencies.

Ground planes are a means to an end. They're not mandatory. If you end up deciding to use PCB with more than two layers, it might be cheaper to build two PCBs and stick them together (underside to underside) with a bit of glue.

Personally, I'd raid the local junk yard and see how others have done this. The Fuba antenna has about 20-odd components jammed into about 2 cc volume.