Hello all!

I am considering converting my giant escape 2 to bullhorn bars.
My current flat bars only offer one hand position and feel really wide, two aspects I don't particularly like as I am more used to drop bars.

Currently on my list of components to acquire are the bars themselves, a set of tt style brake levers, and a set of caliper brakes (the bike came with linear pull brakes for some reason *rolls eyes*). My stem has a 31.8mm clamp so I need bars that will fit. I like the look of the tt style bar end brakes, but I have so far not been able to find thumb shifters with a 23.6mm clamp that are also compatible with the Shimano Altus derailleur the bike has. As you can probably tell, I am somewhat lost, and I have no real knowledge of good online retailers for bike parts besides amazon.com.

If anyone with knowledge of such products could give me some suggestions I would greatly appreciate it, cheers!

Are you planning to put the shifters on the flat section near the stem, or out on the horns?
If by the stem, some Paul's thumbies and a suitable pair of bar end shifters should sort out shifting for you.
Don't think thumb shifters would line up well out on the horns.
If your bike came with linear brakes, it probably has fairly good clearance. Means you'll need long-reach caliper brakes.
Expect to lose a fair amount of brake performance.

I'd prefer to try bar end shifters in their regular position either together with JTEK Aerobrake Jtek Engineering AeroBrake bar end shifter mounted brake lever
Or bar end shifters together with cross/interrupter levers mounted in reverse.

You can attach bar ends inboard of your grips (google this). No need to change any other parts. I put them on mine and the bull horns (no more bar "ends") are 51cm apart centre to centre.

Switch to a set of Velo Orange Crazy Bars. You'll have 4 different hand positions (including "bull horn") and won't have to change levers or shifters. They're brilliant.

Give mustache bars a chance. We've converted many drop bar bikes to m'bars and they give multiple hand positions. Drop bars really don't give multiple comfortable hand positions.

The drops just typically aren't a position most cyclists can comfortably reach. Mustache bars are very comfortable.