What size and type of wire is recommended for new wiring from a meter to the electrical panel / breaker box?

Far too little info. and many things sound strange:

Permit in hand?

Talk to the local Inspector.

They gave you a service without inspection, or is this a 'temporary construction service'?

A separate meter for a garage only?

Or do you plan more structures in future from this service?

(If so since the trenching of the service wire is a big job,

size the buried conductors for the whole projected load.)

If the load is only lighting and that heater, 3 # 8 underground

cable is enough. (at least 24" deep.)

If you are putting in a shop, add the load of the largest machine(s)

you will be using at any one time along with the heater.

Add up all the load likely to be used at the same time and 5 amp.s or so for lighting.

#8 - 45A.

#6 - 60A.

#4 - 80A.

That 90' is just on the edge of where you would go up a size for

voltage drop.

If your load is 'close' go up a size.

The short answer to your question is YES. There is no reason to completely replace the romex cables. As long as you match the wire size and have a tight connection, there will not be any heat build up. If they still reach the inside of the breaker panel, extend the wires using wirenuts inside the panel. If they no longer reach, then install a junction box, run the romex into the j-box and, again, extend the wires to the breakers using wirenuts. Make sure all of your connections are tight and won't pull out of the wirenuts. If any of the wires are stranded, make sure that there aren't any stray strands sticking out. Covering the splices with electrical tape won't hurt either, but is not required. Whenever I open a panel, I always go through it and tighten all of the branch circuit connections. I do this because they loosen over time. I opened a panel once and found a neutral wire glowing in the dark space. About 3" of the insulation had melted back and left the now bare copper discolored. So I cut the wire back and re-terminated it. Then I made sure all of the other connections were tight. I have checked them all ever since. For the feeder coming in, you will need insulated tools to tighten those down. You should be able to leave them alone until you actually have a problem.

Where are you installing the electrical meter?

You only need to run the wire from the meter to the panel. Based on the size of the panel you are looking at 100 amp service.

Based on your lack of knowledge I am not sure this is a project you should safely undertake.

Where I live the power company runs the wire from the pole to the meter. But who is going to hook up your meter? You might want to consult with an electrician and have him hook up the meter to the panel.

The size of wire is determined by the amp size of the meter and panel. I can only tell you what the NFPA code recommends or what is code in my state. Also are you aware of the grounding requirements for your local area. Local codes often differ slightly from the national code, you need to consult with your local building inspector or zoning commission. I am sure a permit is required for this work. The power company will not make the connection without the permit.

8 gauge wire is not enough for a 125 amp panel and a run of 90 feet.

You need to get this right. Call an electrician to make the connections between your panel and the meter.

If you are sure you know what you are doing for the remainder, then go ahead with all of that. Be aware that a mistake might mean your newly built garage goes up in flames.

They have an amp chart at Home Depot . The box you use will take a certain Gage wire to fit the holes . The box will tell you what that is . Go copper . Not aluminum.

2/0 copper check lugs in meter base to assure fit pwr co will provide proper size,

call an electrician