Hydraulic hoses

Shimano BR-M3050 calipers are from the Acera line: https://bike.shimano.com/en-EU/product/component/acera-m3000/BR-M3050.html

Normally I'd point you to the Shimano specifications page which tells you the brake hose kit required, however the BR-M3050 calipers are missing. I suspect that the BR-M3050 calipers are new and replace the BR-MT200 calipers in the Acera line up.

I'd try working through a local bike repair shop to find out which hose is compatible, then try contacting Shimano directly.

The BH59 or BH90 will work. You will need to trim the hoses to length (as they always come excessively long), and install them with the correct hydraulic fittings. There will be a T-shaped insert that needs to be hammered into each end of the cut hose, a brass barrel-shaped piece that slips over each end, and a special nut that holds everything together and creates a seal. You will also need to bleed the brakes afterwards.

If you don’t feel comfortable doing all this, it might be best to leave this to a shop. Screwing up a brake installation, although the results will be obvious (no power or a leak), could be very dangerous.

Your question is unclear; a frame would normally be just a frame, without calipers or levers.

From your question it is therefore not clear whether you have the levers or not.

M3050 is a basic caliper with no special features.

If you buy the cheapest set of Shimano brakes, which would be MT200, then this would be the same quality as M3050, but would come with (if you buy a complete brake) hose, lever, new caliper, and new pads. In addition, typically if you are careful when fitting these will not require bleeding, whereas if you buy new hose then you will need hydraulic oil, and tools for bleeding.

So your calipers may have little value to you since the levers and hoses will almost certainly cost as much as buying a whole new brakeset, while the hoses alone will cost nearly as much as a full brake set.

As far as hoses go, you can use BH59 or BH90, which are the same outer dimensions, different internal dimensions (BH90 is more expensive, and more rigid). You need to match the fittings then to the lever & caliper (since the hose is the same external dimension, you can use either BH59 or BH90 with any lever & caliper combination, with the correct (BH59 or BH90) insert). The M3050 caliper is a straight fitting (much more expensive calipers may be banjo), whereas any lever is likely to be straight.

This is the BH59 kit for 'SS' (i.e. straight-to-straight)

https://bike.shimano.com/en-EU/product/component/shimano/SM-BH59-JK-SS.html

which is sold in 1m, 1.7m and 2m dimensions. You will probably need something like 1.5m and 0.9m for back/front, so it is not possible to use both 2m for two brakes.

Installation manual is here:

https://si.shimano.com/api/publish/storage/pdf/en/dm/BR0005/DM-BR0005-16-ENG.pdf

Note that if you find a 'jk' model that refers to j-kit, which is a pre-filled hydraulic hose system intended to make brakes easier to fit and shorten without oil loss/bleeding; this is most benefit on road bikes with under-tape hose, so that a dangly bit can be re-attached. However it doesn't matter for you if you have it or not

If you buy hose by the metre, from a bulk supplier, then it might well be cheaper than buying a set such as I listed above. The olive and inserts are inexpensive, so possibly you could make it work if you did it like this. You would need 2.5m, minimum, for two brakes, possibly more depending on frame/fork. You would also want to buy a hydraulic hose cutter (you can use a knife, but a cutter is cleaner), and then hydraulic brake mineral oil (Finish Line, Shimano brand, maybe others should be ok)

If it is not particularly worthwhile reusing your (used?) pads, calipers, then you might well end up with a totally different set of brakes.

M3050 would have been paired with ST-M3050, which is 9-speed and has MTB-style (short brake levers). MT200 levers are longer, which for MTBing makes 1-finger braking more difficult - Shimano gives long levers on their cheapest brakes.

If you have these M3050 brifters still, they are not really worth replacing, since 9-speed is fine.

If not, then you might well choose a totally different brakeset - some features of more expensive brakes would include things like 'servowave' levers, fancy pad choices, 4-piston brakes, and so on.