Surprised nobody has replied, this is a very common thing to do. Lots of options,
It depends if you want to race and win , or just enjoy day sails. For racing you want minimum diameter line with the cover stripped from the portion that stays up the mast with sails raised. Reducing wind drag is key. That's why I still use my origanol wire halyard, still in ok shape after nearly 50 years. It's the most areodynamic option.
For a Genoa halyard wire is not so good as gets abused alot.
For racing I would suggest 1/4 inch polyester covered dynema. Samson warpspeed is a good choice. However there are many other brands and grades. Warpspeed is mid grade.
You can do your own splicing and stripping of the cover. Lots of info how to do it on YouTube and also at manufacturer sites, new England ropes, premium ropes , Samson all. Have the info.
Tons of places to buy the stuff, Mauro pro and Vela sailing are two very good sources with some educational info. Discount sources like defender Marine and Hamilton Marine are good if you know what you want. West Marine is ok if the have a sale going.
When you switch from wire you likely will need to replace the block up the mast for the Genoa halyard, the old blocks were meant for wire are ussually to narrow and a vee shape, for line you want a round shape. The main halyard sheave at the top of the mast is probably fine, just inspect to make sure it spins freely with the size line you choose.
If you only cruise or race slowly, use 5/16 diameter as this is easy on the hands. Leave the cover on if you like to save some work.
Choose colors that makes sense with your other lines so it's easy to identify lines by color. I like gray for main, green for Genoa. Blue for spin up, red for spin down. Yellow for spin halyard. But there is no real standard code for colors
Jim Knape
Lickety Split 1575