Best SSD Brand for Windows 7 AMD 8350 Build

Double sided tape ? Just install the SSD into a 2.5 bay and most cases are coming with those now and if not there are plenty of adaptors out there and the SSD does come with screws and screw holes.
The Samsung 840 128 gb would be the best choice followed by the 830 and then the OCZ Vector which is a new release and is much better then the Vertex 4. I know that price can be a concern but if it were possible within your budget to get a 256 gb SSD it would be the best solution for an OS drive. With as 128 gb drive you will have to manage your space so as to not go over 80% capacity.

I got a 256gb but returned it due to having more money buying a 128gb and then a 1tb 7200rpm

Yes , like I had said if it's a budget concern then you have to get the best setup that you can for the money that you have.

the 840 has a lot of bad reviews and alot of failure rates

i have a amd 4 core 3.6 gzh and i have the vertex 4 and i get a 9 sec bootup time and it runs great and this is my 2nd vertex 4 in my newest pc i built the 3.6 gzh i have a 128gb drive , i first put a 60gb vertex 4 in my 7year old dell with amd chip set i got the low gb ssd drives for the low cost so i have {2} 2 tb external hard drives that hookup to sata ports as they cost 60.00 for each so i just download and transfer files to the external drive was a lot more cost efective for me

Is the vertex reliable in your opinion

Are you looking at the 840 with TLC and not the 840 Pro with MLC ? I have the 840 Pro and it works as good if not better then the 830 that I have.

I would say avoid the 840 TLC, as it's the first TLC SSD in large scale production so TLC's longevity is still unproven. Intel 520, Samsung 830 are excellent options. Aside from that Kingston HyperX is also a good option. Really any SSD will be a huge improvement over a HDD. Between SSD's you may not notice a difference unless you're doing really intensive read/write. Just check reviews before you buy and make sure there aren't any widespread issues.

840 Pro would be pretty nice - I am using a 180GB Intel 520 paired with a 1.5 TB HDD in my 8150 rig. I have used the 830s in a lot of builds and the 840 pros are a significant upgrade in terms of speed.

Check the skus that are available when you're ready to pull the trigger - most manufacturers have an options which will include a 2.5 to 3.5 adapter plate/bracket

+1 so vertex 4 or 830