If I understand correctly, you previously had a recessed medicine cabinet that you removed and now there is a hole in the wall? Well, you patch it. You cut out the hole such that you can properly anchor a new piece of dry wall into the hole and hit studs. Then you use mesh tape and drywall mud to secure where the pieces meet and feather out so that the patching is no longer visible. Then prime. Then paint. This is doable but I have found it to be difficult to get a perfect looking wall if you're inexperienced. Might be worth it to pay someone to patch it up for you.

I would suggest going with neutrals with beige/taupe/white with anything that is hard to change. Maybe switch the a A new counter top with neutral Formica and a white sink. You would be surprised as to how inexpensive Formica is. But of course then there is a new sink, faucet and a bit of plumbing work.Go to a home improvement store and ask them lots of questions A friend put in bead boards and painted a soft white in bathroom, I think it looks nice. But they are usually glued and nailed so if you ever get tired of it it would mess up the drywall underneath. I've seen wallpaper that looks like beadboard. But I hate wallpaper myself. You could just do a chair rail and paint the above and below in different colors. As for you light, you probably have one of those that is kind of built into the medicine cabinet and have the round bulbs, I am not sure what to suggest, but they are usually separate from the cabinet. Maybe the home improvement stores have a suggestion. I wanted more storage in my bathroom but didn't want to install medicine cabinet, I have a large plain mirror over sink. Plus wanted deeper storage. I found a white stained kitchen cabinet and installed over toilet. It was a discontinued item so got it cheap. It took some getting used to, afraid it would be too big and bulky, but being whiteish made it not seem so. I had been watching for something for at least a year.

When you say low budget are you talking $100 or $500 or more? The reason I ask is that you can replace the vanity and medicine cabinet and light for under $500. I lucked out and did a rental property I have with things I found at Home Depot in their clearance section. $200 for vanity, light and medicine cabinet. The only thing I had to do to them was change the hardware on the vanity to brushed stainless to match the room. As for the counter top, find a granite fabricator and ask about leftover granite or solid surface material. They will often cut it for you at very inexpensive rates as they have no use for these smaller pieces. From personal experience, I've used Valspar paint in 3 rooms recently and the paint after being applied matched the chips exactly. So if you like what you see on the chips, you should be OK with the paint choices. I love beadboard in bathrooms and think the white beadboard really brightens up the room. Don't worry too much about lighting until after you've picked out a new light. The type of lighting you've had in there really doesn't give off enough light and it's something you can keep in mind when selecting the new lighting. There are some great deals online for lighting, I just did 3 bathrooms for under $160, all were on sale and found an online coupon for an additional 30% off on LampsPlus. The same lights, 2 of them were almost twice as much as big box stores locally. It's easy to save money if you take your time and look around. Check Ebay and CL, too. I've had friends who found great deals on CL due to the unfortunate situations people find themselves in due to our economy. Have fun and good luck with the remodeling!

Are you replacing the floor tile completely? If not, you may have a problem. The current tile may end at the vanity edge. With the new mirror, be sure to use only water - no glass cleaner - to clean it. I know that with mine, using glass cleaner will void the warranty. Cleaners wicking up behind the glass is said to be the cause of the loss of silvering you see on the edges of mirrors. A spritz of water and a microfiber cloth does the trick. With so many designers insisting that you should not put two sinks in a 60" vanity, there must be more than a few to see. Just for grins, check out Wayfair, where you can do a search for a vanity that size, then specify one sink. See what is out there to buy online if you have not looked already. Once you have seen them, you can look for local distributors of that line if you do not like to purchase such large items online.