I've never heard the expression "Grease Man" before. Maybe it's like Groundskeeper Willie telling Lunchlady Doris to grease him up before he goes into the HVAC system.

Personally, I would save the eyes and ears for later. At the start, they're easier to replace with gear. Down the road, they're easier to upgrade incrementally. That saves some nuyen. And I think some of the eye mods conflict with Hawk Eye.
I would ditch the partial cyberlimbs and go for for full limbs. Drop the Alphaware if you need to free up nuyen. You could even go Used, which is a hit to your Essence but allows you to access some higher Availability upgrades, like Armor 3. Armor 3 in each limb = instant tank. Plus, speaking of tanks, you could put the Internal Air Tank into one of the limbs to help balance the Essence hit. Maybe the commlink too.
Your limbs might run into your Wired Reflexes. An extra initiative die is nice but it's not critical. You could also consider Reaction Enhancers instead of Wired Reflexes. If you get them Used, you'll not only save Essence but nuyen too. Your average initiative boost won't be as high but you'll be better off for dodging and Reaction tests (like driving, should you learn to do that).
Boost those hydraulic jacks if you can, not so much for the jumping (which is underwhelming) but for doing superhero landings like a boss when you're falling.
Agility 6 and Strength 6 are the minimum, but half the reason to get cyberlimbs is to get Agility 9 (and Strength 9 if possible) for a pittance. I'd make that a high priority. You can add a spur to one of your cyberlimbs for some Grade A stabby-stab. That also saves you having to split skill points between Blades and Unarmed Combat. Just go with the latter with the Cyber-Implant Weapon spec you have.
Depending on your GM, you could dump Strength and/or Agility from your attribute point spending because your cyberlimbs will represent 99% of your Strength and Agility tests. I suppose a GM could complain about your core strength, but that's not well-represented in Shadowrun mechanics.
Perceptive is a bit expensive unless you also have Assensing or something else it can apply to.
That's what I have time for. Have fun!