Been thinking of starting a character with Guns, Melee, and Sneak as my Tag skills. Will I be gimping myself if I put hardly no points into lockpick, science, and speech? If so, how much would I miss out on? A majority of the content?

Lockpick, Science, and Speech are immensly valuable if you like alternative ways. Lockpick and Science are valuable if you like to find loots and shortcuts through places. Speech is valuable as it unlocks more dialogue and makes it easier to convince people of things.

At LEAST have a lockpick skill of maybe 30 or something, It's a useful skill for loot.
Science... Is okay to miss but there are some things that can be very helpful like turret controls and downloading keys/passes.

Dial down strength and add the points to intelligence and charisma, apart from anything else it will force you to be efficient at selling stuff rather than carrying it about and as the game progresses you can add to strength or get a companion.

Also pick up jumpsuits in 101, they can add useful points to lockpick, science and repair. They're light too.

I wouldn't do that, Intelligence of 6 and Charisma of 4 is plenty.

I would keep Strength 6 to save a perk and extra 20 lb carry weight.