What shall I learn?

My advice is 'Learn the instrument you really want to play!' If it proves physically impossible for you at least you have had a go and you can then compromise.
But... here is some guidance:
soprano sax - ianalto sax - iantenor sax - ian
Of all the woodwind and brass instruments the saxophone is almost certainly the easiest to learn. It is particularly suitable foradult beginners. If you can already read music it is an instrument where you can achieve a great deal in a short time.
I would usually recommend alto saxophone to start on. It is the easiest to find and also the cheapest to buy (both new and pre-owned). A serviceable Chinese instrument can be picked up new for around £325. Small (and determined) children sometimes start on a curved soprano if they can't wait to grow into an alto. Some adults may wish to start on tenor just because they love the sound.
Here is a clip of Charlie Parker playing Summertime:
trumpet - ianpocket trumpet - ian
Many young brass players start on trumpet or cornet. These instruments are very similar. The trumpet is used in classical/big band/jazz/wind band contexts. The cornet is used almost exclusively in brass bands.
The small mouthpiece and high "resistance" does not suit everyone. Sometimes a larger brass instrument is better for mature beginners.
An adequate cornet or trumpet can be purchased new for less than £200. A local brass band may loan a cornet free of charge if you commit to playing with them when you have reached an appropriate standard.
Here is an example of trumpet solos from the film 'The Princess and the Frog'. Listen hard for the trumpet all the way through! 
This is Philip McCann playing a cornet solo with the Black Dyke Mills Band:

flugel - ian
The same pitch as trumpet (cornet) but a larger bore. Found in jazz and brass band contexts. Tuning can be a little tricky.
This is Chuck Mangione playing "Feels So Good" on the Flugelhorn:

  euphonium - ian
The so called "background brass" which does not do justice to their potential as solo instruments.
The tenor horn is pitched in the Eb and has a slightly larger mouthpiece than the flugel horn. This makes it rather easier to blow.
The Baritone and euphonium are pitched in Bb, have significantly larger mouthpieces and are relatively easy to blow. The difference is in the bore size. The euphonium is larger. These are almost exclusively brass band instruments.
The tenor horn is a useful prelude to learning the french horn.
The euphonium or baritone can be good training for trombone or bass tuba.
All are fine instruments in their own right. It may be worth trying to obtain any of these on loan from a local band.
The following clip is of Lyndon Baglin playing Hartman's "Rule Brittania" with the Cory Band on the Euphonium:

trombone - ian
Commonly found in two "flavours", tenor and bass. Confusingly these are exactly the same pitch (in modern times). The bass is built with a wider bore giving it a "fatter" sound and may have one or two valves extending the range downwards.
The tenor may be found with or without a valve, and in a variety of bore sizes, for different styles of music.
Again you may wish to try and borrow an instrument form a local band. Chinese instruments can be purchased for between £175 and £350 depending on bore size/valve.
Probably best to learn on a tenor and take up bass later if you really want to.
This is Roy Williams playing Old Folks on the trombone:

french horn - ian
A very long narrow tube.
 A very wide bell.
A small funnel shaped mouthpiece.
 Played with the left hand.
Usually pitched in F/Bb.
This instrument is very different from all the other brass instruments.
It can be learnt as a "first instrument" but I would not recommend it as pitching can be difficult.
Many people graduate to french horn after laying strong foundations on trumpet or tenor horn.
I would always recommend a specialist teacher if you can find one!
This is not an instrument which you will find easy to borrow as it is not featured in brass bands. Get advice before buying one as there are a variety of designs and pitches and these vary with regard to playability / suitability for a novice.
This following clip is of Dennis Brain playing Mozart's Concerto No. 4 in Eb major:

  tuba 2
A term covering a whole family of instruments from the euphonium (tenor tuba) through F, Eb, C and Bb getting progressively bigger, heavier and lower.
Eb and Bb instruments have traditionally been most common in the UK. There are two of each in British brass bands.
The Eb tuba has been the instrument of choice for orchestral and freelance players in this country since the mid 1950's when it effectively superseded the smaller F tuba.
C tuba is now becoming increasingly prevalent in an orchestral context following the lead of players in the USA.
I would very strongly suggest learning on an Eb instrument for many reasons. A four valve instrument is essential for any use except absolute beginners or smaller children.
Tubas are expensive. Good tubas are very expensive unless you are very lucky and find a second-hand treasure. Borrowing one from a local band may be the best option.
Tuba players are hard to recruit and you may find yourself very popular!
This is a clip of John Fletcher, who was widely regarded as one of the UK's best tuba players, playing "Flight of the Bumblebee":

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