My suggestions are this
If you want to gain a lot of SP through Logi-ing then

1. Grab a Drop Uplink for public matches. All non squaded blues can also spawn on your uplink which will net you about 25 WP per spawn, but be careful where you drop your uplinks, pick areas that your team can defend well and not be easily overrun, or drop them in locations where your team will have the advantage of being able to overrun the opposition.

2. Take the Nanite injector. This is a huge WP boon for a Logi and really should be key in how your logi operates. Sure Repping is what your should be focusing on but if a squad mate goes down and you can safely get to him not only do you earn his respect for 5 minutes, but you also save your squad a clone, and get 60 WP.

3. Use your Repair Tool more than your Assault Rifle or whatever weapon you use. Find a Heavy and follow him you can get constant Triage Repping scores for prolonged repairs on them, and you can score a guardian bonus whenever your heavy kills a guy and you have a repair stream on him.

Other than that know when you can and can't engage targets. if you have lots of guys firing on a single target then lend a hand, odds are you will score an assist or even the kill.
A good logi survives the fight and sticks with his squad, an even better logi knows when to fight and when to heal and can balance the two.
E.g- My CEO is a devout logi, he goes most games in double digits with one of two deaths and near on 1600 WP every time....he's scary man, really scary.

1. I don't think I am skilled yet to use drop links though I plan to eventually get into them.

2 and 3. I currently have the Nanite Injector (militia), repair tool (militia), and the compact nano-hive. Though I don't seem to get SP when people stand in the nano-hive though which is weird.

Other Stuff: I tend to keep my repair tool out more often if the blues seemingly are working together. I push the "up" button a lot especially in the beginning to see if their are multiple people from the same corp together and find them during the battle and just heal and work with them. Other times it is just a gaggle and no one on my team seems to have a plan and I try to do the best that I can with it.

I don't run out into the open to revive someone until the enemy is dead or at least thinned out. I am still getting use to the Mass Driver so sometimes I get an incredibly lucky kill from long range and in others I kill myself when trying to shoot the enemy like 5m from me >.<

I mostly play with blues since I don't have a mic though I can hear what my squad is saying. I tend to play just in publics so my corp can do their business.

I average about 5/1 to 5/4 for K/D with an average WP of 600 and I get roughly 5k SP every match and 120k to 230k ISK. Running as a logistics with a Tsunami Mass Driver (I bought the Mercenary pack). I have Logistics Type-I suit. I have the militia versions of most of my gear because I am saving to get Minmatar Logistics III. I try to revive/repair those that I come across if it is safe to do so.

It just seems slow for me in gathering WP in order to increase my skills. Any helpful tips? I generally end up between 3rd and 6th in most of my games.

A well-placed and hidden Drop Uplink can net you over 100 WP easily. Well-placed Nanohives can easily net you 50 WP apiece.