I have a 1984 with the automatic transmission: 700-R4 (4L60). My father and I are dropping the transmission due to some slight leakage, and are going to replace all the external seals. We were hoping for a kit with all these components, and have found the kit offered through Classic Transmission solutions (Product #CT301518).

Any thoughts or opinions or suggestions? Please and thank you. 

I would try to determine WHERE the leaks are before removing the trans. What normally starts out as a "simple re-seal" often turns into much more.

The  "External Gasket & Seal Kit" you listed has far more than just "external" seals. If you plan on removing the pump and replacing the gasket and o-ring on it, then that is a little more involved than just popping the front & rear seals out and replacing them. Not something I would recommend unless you have the skills/tools to do it. Not knowing your level of mechanical capabilities, I'm just giving a small warning about opening the trans up if you have never done it. However, if simply replacing the front & rear seals, governor cover seal, pan gasket, speedo seal, filler tube and TV cable seals, shift shaft seal(requires a special tool to remove safely unless you remove the shaft from trans from the inside), those are fairly straight forward, remove/replace. The pump gasket/o-ring, and the servo cover o-rings is where it gets more technical, and will require some care. I unfortunately get to repair many mistakes made by folks that weren't really prepared to do what they thought they could do. Again, I have no idea of your particular skill set, so...just giving some advice. 😉

Joel Adams  
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"Money can't buy happiness -- but somehow it's more comforting to cry in a CORVETTE than in a Kia"

Thanks! I greatly appreciate it. We had not planned on necessarily using all of the seals that came on the kit, just the basic and accessible externals. If it get's beyond our comfort level, I have wrapped my head both mentally (and financially) around the fact it may take someone with more skills. But we figured it may be worth our effort to try and do some basics to resolve the issue, and maybe crack a few jokes along the way. Thanks for your time.

Any opinion one way or another on the particular part we chose? Any other directions I could look?

The kit you listed will have everything you need to do as much as you feel comfortable doing. Truth is, unless you can absolutely determine the trans is leaking from the front/torque converter area, you don't even need to pull it to replace the rest of the seals. Only the torque converter(front) seal, and pump gasket/o-ring require removing the trans to replace. 

Joel Adams  
My Link

    
(click for Texas-sized view!)             NCRS

"Money can't buy happiness -- but somehow it's more comforting to cry in a CORVETTE than in a Kia"