Many options exist, depending on your budget:

• IPS screen mod for your GB, these are usually not too costly iirc ($60 USD?)
• GBA SP (AGS 001 is frontlit and AGS 101 is backlit), around the same budget for the former, the latter is more coveted and expensive. (EDIT - initial mistake, the GBA is not front/backlit)
• Open source cartreader to dump your carts and saves (and play ROMs wherever you want) - no idea about the budget tbh
• Analogue Pocket, it's great but very likely overkill if all you want to do is play some GB games ($220 USD)
• Depending on how comfortable you are with downloading ROMs (and how ethical you feel that is, given you already have the games), you could just do that without spending a penny since GB games have been preserved and are easily accessible.

There's also a handful of other options (GameCube GB Player, SNES Super GameBoy, etc), but that's likely more consoles and accessories for you to purchase so I didn't mention those in detail.

Pokemon Blue

FYI the internal cartridge battery that's used to save your game is probably either dead or nearly dead!

A multimeter should show the battery at 3.25v. Anything less and it could die any day. Changing the battery isn't too difficult, but it requires soldering.

This is my favorite tool set used to take the one screw out to open the cartridge, to check the battery.

https://www.retromodding.com/collections/tools/products/repair-tools-set

I just put together an FPGBC. It's pretty great and way cheaper than an Analogue Pocket. This video does a pretty good job of the build process and and an overview of the features.

https://youtu.be/ho_Ntx0Fd7U

I bought a GB on eBay but the screen was barely visible. I'm comfortable partially building/

Say less. Replacement screens are plentiful since many (usually with the Color not the grayboy, but still) are doing the IPS screen mods. I'd replace it with an OG screen unless your problem is backlight.

I usually don't recommend reddit but since a total of 0 of them migrated here, check out r/gameboy if you did want to mod it. It's unfortunately a great collection of resources regarding modding GB, GBC, and GBA. Common mods include but are not limited to those backlit IPS screens.

The screen replacement is easy as hell iirc too, I think it's just some clips on a ribbon cable, iirc no soldering required.

Gameboy SP plays GB, GBC and GBA games with a backlight in the screen. If that's not enough, there are plenty of videos online on how to upgrade the SP. Authentic but optimized. Best of both worlds!

I just did something similar. I got given my childhood DMG after my mum found it when moving. It would turn on but the screen was broken. I used this screen and this tutorial. You will have to solder the speaker to the new board.

https://funnyplaying.com/products/dmg-retro-pixel-ips-lcd-kit?variant=31899947761725

https://youtu.be/PDmJ1IJG_Zo

The screen works great now and is backlit. I also bought a $20 copy of tetris to test it. I then bought a flash cart for it. I have the EZ FLASH jnr. Works fine and it saves games. Has a real time clock which you want for pokemon I think.

The only thing I would say is doing the screen modification was annoying. I went back to funny playing and bought the case and parts they have that fit the screen. It's in the mail atm.

I also bought a pack of 4 eneloop batteries and a charger. I considered the clean juice xl battery mod but I don't think I'll use it that much.

I might do a sound mod to it at some point the headphone jack has a lot of hiss. Might just need to replace some caps.

Analogue pocket

myboy or any gb/gbc emulator for pc/android should work fine. you'll also need the rom file for each game. most emulators have controller support

I like my Hyperkin Retron Sq.

The Hyperkin Retron Sq is a nice enough for playing Gameboy and Gameboy Color cartridges.

It's actually fine for lots of Gameboy Advance games, as well.

But, by virtually every account I have seen, the Analogue Pocket is a much better option, for about the same price. If I had been aware of the Analogue Pocket, I would have bought it, instead, or at least first.

You did try to change the contrast on the GB you bought, didn't you?

Modding with IPS screen is fairy easy nowadays with the GBA there is some no soldier options not sure if that is the same with an original dmg.

Another option could be a Epligoue GB operator, which allows you to play your original cartridges on pc.