Based on the pictures, I would opt for a full service upgrade which would include new meter base, riser, feeder wire and electric panel and proper grounding and bonding of said service. If you are going to gradually rewire/add more circuits will want additional capacity available.
This could be a DIY project if you had good support from your local power company (regarding the construction of the service) and from your local AHJ (authority having jurisdiction) regarding permitting and panel construction.
Or you could hire and electrical contractor who could do a full service change in 1-2 days. Then you could gradually install new branch circuits off of the new panel. Where are you located? Someone on this forum could probably give you a ballpark figure for the cost of such upgrade.
Now with the photo what Joed fixed here so we can see it more clear and yeah you have old school 120v 30 amp service you denfinely need new service upgrading the smallest service size they allowed per NEC code for resdentail useage is 100 amp.
There is few ciritcias you have to follow.,,
No load centre in bathroom
No load centre behind kitchen cabents
those two items above that is a major no no per NEC codes.
You will need new meter socket , new riser , new load centre, new ground rods etc
So it can be DIY only if your local codes do allow it otherwise electrician come out and install the correct service that useally a day job otherwise will make a arrangement for longer power outage.
The total cost for service upgrade will depending on the electrician bid and what type of materals they will be using.