COLGeek :
What make/model is your GPU and CPU? If the CPU supports 64-bit operating systems, then install the 64-bit version. Your GPU will be fine and Mint will load the appropriate drivers.
I am not sure what you mean by a "32-bit" GPU, that is why I am asking for the make/model number.
01:00.0 VGA compatible controller: Advanced Micro Devices, Inc. [AMD/ATI] RV620/M82 [Mobility Radeon HD 3450/3470]
processor : 0
vendor_id : AuthenticAMD
cpu family : 15
model : 104
model name : AMD Turion(tm) 64 X2 Mobile Technology TL-56
stepping : 2
cpu MHz : 800.000
cache size : 512 KB
physical id : 0
siblings : 2
core id : 0
cpu cores : 2
apicid : 0
initial apicid : 0
fpu : yes
fpu_exception : yes
cpuid level : 1
wp : yes
flags : fpu vme de pse tsc msr pae mce cx8 apic sep mtrr pge mca cmov pat pse36 clflush mmx fxsr sse sse2 ht syscall nx mmxext fxsr_opt rdtscp lm 3dnowext 3dnow rep_good nopl extd_apicid pni cx16 lahf_lm cmp_legacy svm extapic cr8_legacy 3dnowprefetch lbrv vmmcall
bugs : apic_c1e fxsave_leak sysret_ss_attrs
bogomips : 1596.30
TLB size : 1024 4K pages
clflush size : 64
cache_alignment : 64
address sizes : 40 bits physical, 48 bits virtual
power management: ts fid vid ttp tm stc 100mhzsteps
processor : 1
vendor_id : AuthenticAMD
cpu family : 15
model : 104
model name : AMD Turion(tm) 64 X2 Mobile Technology TL-56
stepping : 2
cpu MHz : 800.000
cache size : 512 KB
physical id : 0
siblings : 2
core id : 1
cpu cores : 2
apicid : 1
initial apicid : 1
fpu : yes
fpu_exception : yes
cpuid level : 1
wp : yes
flags : fpu vme de pse tsc msr pae mce cx8 apic sep mtrr pge mca cmov pat pse36 clflush mmx fxsr sse sse2 ht syscall nx mmxext fxsr_opt rdtscp lm 3dnowext 3dnow rep_good nopl extd_apicid pni cx16 lahf_lm cmp_legacy svm extapic cr8_legacy 3dnowprefetch lbrv vmmcall
bugs : apic_c1e fxsave_leak sysret_ss_attrs
bogomips : 1596.30
TLB size : 1024 4K pages
clflush size : 64
cache_alignment : 64
address sizes : 40 bits physical, 48 bits virtual
power management: ts fid vid ttp tm stc 100mhzsteps