Ah, ok. But with BGA comes expensive 6 or 8 layer PCBs to break out the pins? Worse, .5mm pitch BGAs also require much more expensive small track width and clearance manufacturing capability ruling out the usual cheap vendors? 4 layers would probably be needed for signal integrity, but I believe the price increases sharply above that.
It is possible (though not easy) to route DDR3 x16 interface on a four layer PCB, and this interface will give you a ton of bandwidth (Artix-7 FPGA in speed grade 2 can drive it at 400 MHz, so 800 million transactions/second x 16 bit = 12800 Mbit/s of max bandwidth). These boards are quite cheap at JLCPCB for example ($30 or something like that). For ease of layout I prefer to use 6 layer boards made at WellPCB, and they come at about 130-150$ for ten boards, which is incredible value if you think about it.
DDR2 an DDR3 chips have 0.8 mm ball pitch, and most Spartan-7 and Artix-7 packages have 1 mm ball pitch, so it's possible to route them out without using advanced PCB tech like microvias. WellPCB allows for 3/3 mil traces and down to 0.15 mm vias, and JLCPCB goes down to 3.5/3.5 mils and 0.2 mm vias, both are perfectly adequate for routing out 0.65 mm pitch BGA and up.
Xilinx provides free DDR/DDR2/DDR3/DDR4 memory controller IP for all of its' FPGAs (not all types of memories are available for all FPGAs), you it's got you covered as far as usage goes. Their Vivado IDE is also free for smaller FPGA chips, which includes entire Spartan-7 and Artix-7 lineups.