Get a new counter top even if just a solid wood butcher block one from Ikea .

Ikea also has really good looking cement look laminate counters. Or paint it with blackboard paint. Someone did it on the old Gardenweb and it held up really well.

I have not painted countertops, but from my time on this forum, I would say that in time, one thing or another will fail. There is the added pain of having to be careful when using them. I am not one for putting food on somewhat toxic finishes:)

Painted over previously finished cabinets (especially oak) also have durability problems, especially when done DIY. I say that as someone who actually has some painted cabinets in my home:) So I am not totally opposed to painting cabinets, but I am aware of the limits of painted older cabinetry.

I have been in the position in my life where I wanted to make a space pretty, but did not have a budget to buy many new things. For short term (3 years) and limited investment, you can try anything - even painted counters:) However, if you need these cabinets and counters to still be looking acceptable in 3 - 5 year plus, then you might want to consider some other options.

One thing which helped me was that my style was always on the cottage / vintage side, and it is much easier to make older surfaces work with that style. If your style if very contemporary, modern, it will be harder to work with the older surfaces.

I would not put granite or quartz on older, painted oak cabinets. However, there are some very good looking laminates now - and still the price may be too high. Two lower priced options are "stock laminate" and butcher block wood. Stock laminate comes in pre sized pieces that will need to be trimmed to fit - so a little more work labor wise, but they are inexpensive. Stock laminate often comes in black and this would look nice with white painted cabinets.

I did put quartz on my 20 year old oak cabinets - but the cabinets were in great shape, I refinished most of them, and I new I was not going to get rid of them in the next 10+ years.

My main kitchen:

https://www.houzz.com/photos/my-pics-work-in-progress-phvw-vp~110720042

Another option is butcher block counters. Some care needs to be taken of the wood - especially around the sink, but home center butcher block is also not expensive. I had home center butcher block on my island for many years and it held up very well.

Butcher block:

Both of the above kitchens also make use of some open shelving. It is not everyone's thing and does require more cleaning, but removing some upper cabinets for shelves may help you achieve a prettier kitchen - if you can keep it up.

I wanted to put a kitchenette in my basement, but was on a very tight budget. The electrical and plumbing were already present. I manages for about $1000 - refinished some of my stored in the garage original 70's cabinets (got creative when some of the doors proved beyond repair), used home center stock laminate counters, textured, paintable bead board wallpaper, and my old kitchen sink (which was in great condition). The uppers had been painted and put in the laundry room, so I made some shelves out of fir joist for the kitchenette. About $600 of the cost was labor - I don't instal cabinets or do major plumbing on my own:)

https://www.houzz.com/photos/my-pics-work-in-progress-phvw-vp~65270573

This guest cottage kitchen is a favorite of mine - found on the French Country Cottage Blog:

This kitchen was also done on a very tight budget and looks great - more info here:

https://www.frenchcountrycottage.net/2012/08/petite-cottage-kitchen.html

If you like a cottage style and want to post some pics of your kitchen, I might have some ideas for you.

Save the money and replace the counters. There are some man made stones that are very reasonable for cost and some nice laminates that are much better looking than they were 10-20 years ago. How big is your kitchen? How many feet of counter? How about a photo of the current kitchen?